Variable Coefficient EquationsExpected Educational ResultsVariable Coefficient EquationsDefinition: Variable-Coefficient EquationTheorem: Existence and Uniqueness of SolutionsDefinition: Cauchy-Euler Equations, a.k.a., Equidimensional EquationsInvestigation 01CC 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.

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Suppose , , and are continuous on that contains . Then, for any choice of the initial values of and , there exists a unique solution in the interval to the IVP , , .

For real numbers , , and , . Cauchy-Euler Equations are **equidimensional** because , , and have the dimensions (i.e., units).

Is a solution to ? Explain.

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**Last Modified**: Thursday, 14 October 2020 11:39 EDT