Hello, I am having trouble finding a simple direct application of differential e

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Hello, I am having trouble finding a simple direct application of differential equations with variable coefficients or cauchy euler differential equations or variation of paremeters method. Could someone please give a good example that has been worked out. For example something dealing in physics, finance, biology, etc... I've found plenty of examples for laplace transforms but not for differential equations with variable coefficients. Please give me examples that are detailed. Thankyou for your time.

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