Variable Coefficient Equations

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:

Expected Educational Results

Variable Coefficient Equations

Definition: Variable-Coefficient Equation


Theorem: Existence and Uniqueness of Solutions

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 , , .

Definition: Cauchy-Euler Equations, a.k.a., Equidimensional Equations

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

Investigation 01

Is a solution to ? Explain.


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