Find a general solution to the Cauchy-Euler equation x°y'"' - 8x²y" + 9xy' – 9y = x², x> 0,

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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### Cauchy-Euler Differential Equation

**Problem Statement:**

Find a general solution to the Cauchy-Euler equation:

\[ x^3 y''' - 8x^2 y'' + 9xy' - 9y = x^2, \quad x > 0, \]

given that \(\{x, 6x \ln (4x), x^9\}\) is a fundamental solution set for the corresponding homogeneous equation.

**Solution:**

\[ y(x) = \_\_\_\_\_\]

(Simplify your answer.)

For further steps and detailed explanations, please [click here](#).
Transcribed Image Text:### Cauchy-Euler Differential Equation **Problem Statement:** Find a general solution to the Cauchy-Euler equation: \[ x^3 y''' - 8x^2 y'' + 9xy' - 9y = x^2, \quad x > 0, \] given that \(\{x, 6x \ln (4x), x^9\}\) is a fundamental solution set for the corresponding homogeneous equation. **Solution:** \[ y(x) = \_\_\_\_\_\] (Simplify your answer.) For further steps and detailed explanations, please [click here](#).
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