# Worksheet: Linear Homogeneous Differential Equations with Constant Coefficients

In this worksheet, we will practice solving second- and higher-order linear homogeneous differential equations with constant coefficients.

**Q1: **

Consider the differential equation . Suppose that a student determined the solution to be . Based upon this information, is the student correct?

- ANo, the student should have determined the solution to be .
- BNo, the student should have determined the solution to be .
- CNo, the student should have determined that there is no solution.
- DYes, the student did not make any errors.

**Q6: **

Suppose there are differentiable functions and , defined for all real numbers and satisfying and .

From the derivatives, what can you deduce about ?

- A is a constant function.
- B is an exponential function.
- C is a hyperbolic function.
- D always equals 0.
- E is a trigonometric function.

It is known that every function that satisfies is a combination for some constants and . Find all functions satisfying and , where .

- A and
- B and
- C and
- D and
- E and

Sketching graphs of the functions above suggest that for some constants and . Find these constants, where .

- A,
- B,
- C,
- D,
- E,

**Q13: **

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

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- E

**Q14: **

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

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- B
- C
- D
- E

**Q15: **

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

- A
- B
- C
- D
- E

**Q16: **

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- E

**Q17: **

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**Q18: **

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- E