GRE Subject 2026 Practice Test Maths Differential Equations Free Quiz 2

11. What is the solution of y'' - y = 0?

A. y = C1 cos(x) + C2 sin(x) B. y = C1 + C2 x C. y = C1 cosh(x) + C2 sinh(x) D. y = C1 e^x + C2 e^(-x)

12. What is the Wronskian used for?

A. Integration B. Linear independence C. Differentiation D. Transformation

13. What is the Laplace transform of f(t) = 1?

A. 1 B. s C. 1/s D. 1/s^2

14. What is the Laplace transform of f(t) = e^(at)?

A. 1/(s + a) B. 1/s C. 1/(s^2 + a^2) D. 1/(s - a)

15. What is the Laplace transform of f(t) = cos(at)?

A. s/(s^2 + a^2) B. a/(s^2 + a^2) C. 1/(s^2 + a^2) D. s/(s^2 - a^2)

16. What is the inverse Laplace transform of 1/s?

A. t B. e^t C. 1 D. sin(t)

17. What is the inverse Laplace transform of a/(s^2 + a^2)?

A. cos(at) B. sin(at) C. sinh(at) D. cosh(at)

18. What is the inverse Laplace transform of s/(s^2 + a^2)?

A. cos(at) B. sin(at) C. cosh(at) D. sinh(at)

19. What form does a second-order linear homogeneous ODE have?

A. Nonhomogeneous B. Nonlinear C. Homogeneous D. Exact

20. What method is used to solve nonhomogeneous linear ODEs?

A. Variation of parameters B. Separation of variables C. Exact D. Undetermined coefficients