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2. y' +y = cos x. cos x Answer. y = = + sin x +

2. y' +y = cos x. cos x Answer. y = = + sin x +

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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2 through 8, only even (2,4,6,8)

II. Find the general solution of the linear problems. 1. y' – y sin x = sin x. Answer. y =-1+ ce¯cos x 1 2. y' + y = = cos x. cos x Answer. y = + sin x + 3. xy' + 2y = e-*. (x+1)e-x Answer. y = x2 х2 4. x*y' + 3x³y = x²e%. (х-1)e* Answer. y = x3 x3 dy 5. dx = 2x(x² + y). Answer. y 3 сех — х2 — 1. 6. ху — 2у %3 хеl\x, - Answer. y = cx² – x²el/x. 7. y' + 2y = sin 3x. Answer. y = ce¬2x + -2х É sin 3x – 13 cos 3x.
Transcribed Image Text:II. Find the general solution of the linear problems. 1. y' – y sin x = sin x. Answer. y =-1+ ce¯cos x 1 2. y' + y = = cos x. cos x Answer. y = + sin x + 3. xy' + 2y = e-*. (x+1)e-x Answer. y = x2 х2 4. x*y' + 3x³y = x²e%. (х-1)e* Answer. y = x3 x3 dy 5. dx = 2x(x² + y). Answer. y 3 сех — х2 — 1. 6. ху — 2у %3 хеl\x, - Answer. y = cx² – x²el/x. 7. y' + 2y = sin 3x. Answer. y = ce¬2x + -2х É sin 3x – 13 cos 3x.
8. x (уу' — 1) %— у?. Hint. Set v = y?. Then v' v = v(x). 2yy', and one obtains a linear equation for Answer. y? — -2х + сх?.
Transcribed Image Text:8. x (уу' — 1) %— у?. Hint. Set v = y?. Then v' v = v(x). 2yy', and one obtains a linear equation for Answer. y? — -2х + сх?.
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