Solve y" - 5y" +19y' + 25y = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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How can i solve this differential equation? 

**Problem Statement**

Solve the differential equation: 
\[ y^{(4)} - 5y'' + 19y' + 25y = 0 \]

This fourth-order linear homogeneous differential equation requires finding the general solution for the unknown function \( y \). 

Approach:
- Assume a solution of the form \( y = e^{rt} \).
- Substitute into the differential equation to obtain a characteristic polynomial equation.
- Solve the characteristic polynomial for its roots.
- Form the general solution using the roots of the characteristic equation. 

Further detailed steps and explanations should be provided to guide the student through the problem-solving process.
Transcribed Image Text:**Problem Statement** Solve the differential equation: \[ y^{(4)} - 5y'' + 19y' + 25y = 0 \] This fourth-order linear homogeneous differential equation requires finding the general solution for the unknown function \( y \). Approach: - Assume a solution of the form \( y = e^{rt} \). - Substitute into the differential equation to obtain a characteristic polynomial equation. - Solve the characteristic polynomial for its roots. - Form the general solution using the roots of the characteristic equation. Further detailed steps and explanations should be provided to guide the student through the problem-solving process.
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