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Linear Differential Equation

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Question 1

A linear differential equation of order n is called homogeneous if:

  • F(x) = 0

  • F(x) ≠ 0

  • Coefficients are constant

  • Coefficients are functions of y

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Question 2

The solution of a homogeneous linear differential equation is called:

  • Particular solution

  • Complementary function

  • General solution

  • Singular solution

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Question 3

For the nth-order linear differential equation with constant coefficients, the characteristic equation is obtained by:

  • Replacing y = emx

  • Integrating the equation

  • Differentiating the equation

  • Substituting x = 0

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Question 4

The principle of superposition applies to:

  • Non-linear differential equations

  • Homogeneous linear differential equations

  • Non-homogeneous differential equations only

  • None of the above

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Question 5

Which of the following is a second-order linear differential equation?

  • y′′+3y′+2y = 0

  • y′ + y = 0

  • y′′′−y = 0

  • y2+ y′= 0

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Question 6

If the characteristic equation has repeated roots, the general solution contains:

  • Only emx

  • emx,xemx,x2emx,…

  • Sine and cosine functions

  • None of these

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