GRE Subject 2026 Practice Test Maths Differential Equations Free Quiz 1

1. What is a differential equation?

A. Relates a function to its derivatives B. Algebraic equation C. Linear equation D. Polynomial equation

2. What is an ODE?

A. Partial differential equation B. Linear differential equation C. Ordinary differential equation D. Nonlinear differential equation

3. What is a PDE?

A. Ordinary B. Linear C. Nonlinear D. Partial

4. What is the degree of a differential equation?

A. Degree B. Order C. Coefficient D. Exponent

5. What is the solution of dy/dx = ky?

A. y = Cx B. y = Cx^k C. y = Ck^x D. y = Ce^(kx)

6. What form does a linear differential equation have?

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

7. What is an exact differential equation?

A. Exact B. Separable C. Linear D. Homogeneous

8. What is a separable differential equation?

A. Linear B. Exact C. Separable D. Homogeneous

9. What is the characteristic equation of y'' + y = 0?

A. r^2 + 1 = 0 B. r^2 - 1 = 0 C. r + 1 = 0 D. r^2 + 2 = 0

10. What is the solution of y'' + y = 0?

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