Variable Coefficient EquationsExpected Educational ResultsVariable Coefficient EquationsInitial Value Problems [IVPs]Investigation 07CC BY-NC-SA 4.0

**Author**: John J Weber III, PhD
**Corresponding Textbook Sections**:

**Section 4.7**– Variable Coefficient Equations

**Objective 14–1**: I can identify variable-coefficient equations.**Objective 14–2**: I can find a solution to a homogeneous Cauchy-Euler equation.**Objective 14–3**: I can find a solution to a nonhomogeneous Cauchy-Euler equation.**Objective 14–4**: Given a solution, I can apply the Reduction of Order Theorem to find another solution to a Cauchy-Euler equation.- Objective 14-5: I can find a solution to a Cauchy-Euler IVP.

To solve IVPs:

- Find
- Find
- Find coefficients for
- Use to find coefficients in .

**Example 02**: Solve , ,

**Solution**:

From **Example 01**, the homogeneous solution is .

and

So,

Thus, .

Solve the following IVPs:

- , , .
- , , .
- , , .

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

**Last Modified**: Wednesday, 14 October 2020 11:47 EDT