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Differential Equations Mastery Quiz

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1. Which of the following is the general solution for the differential equation $y'' + 4y = 0$?

2. Which method is typically used to solve the initial value problem for a first-order linear differential equation?

3. What is the solution to the differential equation $\frac{dy}{dx} = 3y$ with an initial condition of $y(0) = 2$?

4. In the context of ordinary differential equations, what does a homogeneous equation refer to?

5. What is the primary use of the Laplace transform in solving differential equations?

6. What is the Wronskian, and what role does it play in differential equations?

7. Which of the following differential equations is non-linear?

8. For a second-order linear homogeneous differential equation with constant coefficients, if the characteristic equation has complex roots, what form will the general solution take?

9. Which technique is best suited for solving a linear differential equation with variable coefficients?

10. In solving differential equations, what is the primary purpose of an eigenvalue?