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Find the general solution of (1) yV – 2y" + y" = 24x² + 12x +8

Find the general solution of (1) yV – 2y" + y" = 24x² + 12x +8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement: Find the general solution of the following differential equations:** 1. \( y^{IV} - 2y''' + y'' = 24x^2 + 12x + 8 \) 2. \( x^2y'' - xy' + y = 4x \ln x \) 3. \( y'' - 25y = 2xe^{5x} \) These equations involve solving for \( y \), where the differentials are taken with respect to \( x \). Each equation includes derivatives of \( y \) up to certain orders, as well as polynomial and exponential terms. These are typical forms in mathematical analysis and applied mathematics, often requiring techniques from differential equations to solve.
Transcribed Image Text:**Problem Statement: Find the general solution of the following differential equations:** 1. \( y^{IV} - 2y''' + y'' = 24x^2 + 12x + 8 \) 2. \( x^2y'' - xy' + y = 4x \ln x \) 3. \( y'' - 25y = 2xe^{5x} \) These equations involve solving for \( y \), where the differentials are taken with respect to \( x \). Each equation includes derivatives of \( y \) up to certain orders, as well as polynomial and exponential terms. These are typical forms in mathematical analysis and applied mathematics, often requiring techniques from differential equations to solve.
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