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MA221 Final Exam - Differential Equations
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MCQs on Differential Equations.

MA221 Final Exam - Differential Equations
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25 Questions

1. Apply the superposition principle to find the solution for
.
2. Using Laplace transforms, find the solution for the following ordinary differential equation.

, where
and

Make sure to also identify the specific Laplace transform
that was used to arrive at your final solution.
3. Find the solution for the following differential equation for
.

4. Find the solution for the following differential equation for
.

5. Suppose that you were asked to find the particular solution
and complementary function
, using the method of inverse operators, for the following ordinary differential equation.


Identify the inverse operator
, which might arise within your solution to this type of problem.
6. Solve the following differential equation by separating it:

7. Find the general solution for the following system of ordinary differential equations.



8. Find the general solution for the following Bernoulli differential equation.

9. Find the general solution for the following non-homogeneous ordinary differential equation.

10. Which of the following statements regarding the method of undetermined coefficients and variation of parameters is true?
11. Find a particular solution for
which passes through the origin and through the point
.
12. Apply the linear differential operator
to evaluate the following expression.

13. Find the general solution for the following non-homogeneous ordinary differential equation.

14. There are a variety of methods borrowed from linear algebra that are very useful for finding the solution for systems of linear ordinary differential equations.One such method includes the usage of matrices.For the following system of linear ordinary differential equations, use these methods to arrive at the solution in matrix form.



15. Find the particular solution for the following non-homogeneous ordinary differential equation.

16. Find the solution for the following differential equation for which
and
.

and
17. Find the solution for the following second-order ordinary differential equation.

where
and
18. Which of the following is a linear ordinary differential equation?
19. Which of the following expressions is of the correct form to serve as a trial solution
for the following differential equation?

20. Find the general solution for this ordinary differential equation with variable coefficients.This is an example of an Euler-Cauchy differential equation (nonzero right hand side).

21. Find the general solution for the following ordinary differential equation using the method of variation of parameters.

22. Find the solution for the following differential equation for
and
.

and
23. The Runge-Kutta Method can be used to approximate the solution for a variety of ordinary differential equations.For the following differential equation, determine which of the following expressions represents an approximate solution using the Runge-Kutta 4th Order Method.

where

Let h denote the step size where …







24. Using Laplace transforms, find the solution for the following ordinary differential equation.

, where
and

Make sure to also identify the specific Laplace transform
that was used to arrive at your final solution.
25. Find the series solution for an ordinary differential equation using the Frobenius method.


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