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dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of variation of parameters to find the general solution of

dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of variation of parameters to find the general solution of

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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h3

For each of the following initial value problems, find the general solution of the ODE and the particular solution of the initial value problem. d²y H1. dy 42+4y = e2*, y = –1 and dr dy = -1 at x = 0. dx dx² Н2. 2- dr2 d²y - 5+2y= 2x², y=7 and dx dy = 1 at x = 0. dx d²y H3. dx2 7 dy 9y x dx ' x? dy 0; у %3D 0 and dx 1 at x = 1. H4. Use the method of variation of parameters to find the general solution of +२ 2d'y dr2 dy – 3y = 4x³. dx
Transcribed Image Text:For each of the following initial value problems, find the general solution of the ODE and the particular solution of the initial value problem. d²y H1. dy 42+4y = e2*, y = –1 and dr dy = -1 at x = 0. dx dx² Н2. 2- dr2 d²y - 5+2y= 2x², y=7 and dx dy = 1 at x = 0. dx d²y H3. dx2 7 dy 9y x dx ' x? dy 0; у %3D 0 and dx 1 at x = 1. H4. Use the method of variation of parameters to find the general solution of +२ 2d'y dr2 dy – 3y = 4x³. dx
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