38 real Differential Equations questions from the Engineering Mathematics bank, as asked in Indian campus drives and tech interviews. Every question has a verified answer and an AI-tutor explanation on placd — free to start.
1. What is Order of a differential equation?
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A.the order of the highest derivative that appears in the equation
B.technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
C.technique that seeks a solution as a product of single-variable functions, splitting a partial differential equation into ordinary ones linked by a separation constant
D.a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
A.Order of a differential equation — technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
B.Order of a differential equation — the general solution of the associated homogeneous equation, carrying all the arbitrary constants
C.Order of a differential equation — the order of the highest derivative that appears in the equation
D.Order of a differential equation — technique that seeks a solution as a product of single-variable functions, splitting a partial differential equation into ordinary ones linked by a separation constant
A.Degree of a differential equation — technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
B.Degree of a differential equation — a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
C.Degree of a differential equation — a first-order equation written in differential form is exact exactly when the partial derivative of the first coefficient with respect to the second variable equals that of the second with respect to the first
D.Degree of a differential equation — the power of the highest-order derivative once the equation is made free of radicals and fractions in the derivatives
A.a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
B.technique that seeks a solution as a product of single-variable functions, splitting a partial differential equation into ordinary ones linked by a separation constant
C.the order of the highest derivative that appears in the equation
D.the power of the highest-order derivative once the equation is made free of radicals and fractions in the derivatives
A.Integrating factor — a linear equation whose coefficients are powers of the independent variable matching the derivative order, reduced to constant coefficients by a logarithmic substitution
B.Integrating factor — a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
C.Integrating factor — a first-order equation that becomes linear after dividing by a power of the dependent variable and substituting a new variable
D.Integrating factor — a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
A.the general solution of the associated homogeneous equation, carrying all the arbitrary constants
B.a first-order equation written in differential form is exact exactly when the partial derivative of the first coefficient with respect to the second variable equals that of the second with respect to the first
C.the power of the highest-order derivative once the equation is made free of radicals and fractions in the derivatives
D.a linear equation whose coefficients are powers of the independent variable matching the derivative order, reduced to constant coefficients by a logarithmic substitution
A.Complementary function — the power of the highest-order derivative once the equation is made free of radicals and fractions in the derivatives
B.Complementary function — a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
C.Complementary function — a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
D.Complementary function — the general solution of the associated homogeneous equation, carrying all the arbitrary constants
A.Particular integral — technique that seeks a solution as a product of single-variable functions, splitting a partial differential equation into ordinary ones linked by a separation constant
B.Particular integral — the power of the highest-order derivative once the equation is made free of radicals and fractions in the derivatives
C.Particular integral — any single solution of the non-homogeneous equation, containing no arbitrary constants
D.Particular integral — a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
A.the order of the highest derivative that appears in the equation
B.a first-order equation that becomes linear after dividing by a power of the dependent variable and substituting a new variable
C.the determinant of solutions and their derivatives whose non-vanishing certifies that the solutions are linearly independent
D.a first-order equation written in differential form is exact exactly when the partial derivative of the first coefficient with respect to the second variable equals that of the second with respect to the first
17. Which term means: "a first-order equation written in differential form is exact exactly when the partial derivative of the first coefficient with respect to the second variable equals that of the second with respect to the first"?
A.Exactness condition — the determinant of solutions and their derivatives whose non-vanishing certifies that the solutions are linearly independent
B.Exactness condition — technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
C.Exactness condition — the order of the highest derivative that appears in the equation
D.Exactness condition — a first-order equation written in differential form is exact exactly when the partial derivative of the first coefficient with respect to the second variable equals that of the second with respect to the first
A.the determinant of solutions and their derivatives whose non-vanishing certifies that the solutions are linearly independent
B.any single solution of the non-homogeneous equation, containing no arbitrary constants
C.a first-order equation that becomes linear after dividing by a power of the dependent variable and substituting a new variable
D.a linear equation whose coefficients are powers of the independent variable matching the derivative order, reduced to constant coefficients by a logarithmic substitution
20. Which term means: "a first-order equation that becomes linear after dividing by a power of the dependent variable and substituting a new variable"?
A.Bernoulli equation — a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
B.Bernoulli equation — technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
C.Bernoulli equation — any single solution of the non-homogeneous equation, containing no arbitrary constants
D.Bernoulli equation — a first-order equation that becomes linear after dividing by a power of the dependent variable and substituting a new variable
A.a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
B.the order of the highest derivative that appears in the equation
C.the determinant of solutions and their derivatives whose non-vanishing certifies that the solutions are linearly independent
D.technique that seeks a solution as a product of single-variable functions, splitting a partial differential equation into ordinary ones linked by a separation constant
A.Wronskian — a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
B.Wronskian — technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
C.Wronskian — the determinant of solutions and their derivatives whose non-vanishing certifies that the solutions are linearly independent
D.Wronskian — the order of the highest derivative that appears in the equation
A.a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
B.a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
C.technique that seeks a solution as a product of single-variable functions, splitting a partial differential equation into ordinary ones linked by a separation constant
D.a linear equation whose coefficients are powers of the independent variable matching the derivative order, reduced to constant coefficients by a logarithmic substitution
26. Which term means: "a linear equation whose coefficients are powers of the independent variable matching the derivative order, reduced to constant coefficients by a logarithmic substitution"?
A.Cauchy-Euler equation — a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
B.Cauchy-Euler equation — the order of the highest derivative that appears in the equation
C.Cauchy-Euler equation — technique that seeks a solution as a product of single-variable functions, splitting a partial differential equation into ordinary ones linked by a separation constant
D.Cauchy-Euler equation — a linear equation whose coefficients are powers of the independent variable matching the derivative order, reduced to constant coefficients by a logarithmic substitution
A.a second-order linear equation is elliptic, parabolic or hyperbolic according as the discriminant formed from its second-derivative coefficients is negative, zero or positive
B.technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
C.a multiplier that converts a linear first-order equation into an exact one so both sides can be integrated directly
D.a first-order equation that becomes linear after dividing by a power of the dependent variable and substituting a new variable
29. Which term means: "technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable"?
A.Method of variation of parameters — the determinant of solutions and their derivatives whose non-vanishing certifies that the solutions are linearly independent
B.Method of variation of parameters — technique that finds a particular integral by allowing the constants of the complementary function to become functions of the independent variable
C.Method of variation of parameters — the general solution of the associated homogeneous equation, carrying all the arbitrary constants
D.Method of variation of parameters — any single solution of the non-homogeneous equation, containing no arbitrary constants
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