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Find the general solution for the following differential equation: y' + 9y = −3√ √ General Solution: y(t)

Find the general solution for the following differential equation: y' + 9y = −3√ √ General Solution: y(t)

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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Find the general solution for the following differential equation: y' + 9y = −3√ √ General Solution: y(t)
Transcribed Image Text:Find the general solution for the following differential equation: y' + 9y = −3√ √ General Solution: y(t)
Given equation y' + 7y= 2 we can write it as y2y' + 7y³ = 7 Let y³ = u and differentiate with respect to tboth sides we get 3y²y' = u' ⇒ y²y = qu' substitute it in equation u'+7u = 7 =u' + 21u = 21 = now this is linear and I. F = ef21dt - e21t Solution will be ux I. F = fI. Fx 7dt le²1t = 21 fe²¹tdt ue²1t e²¹t+C + C = ue²¹t = 21t 112³ + [ = n < replace u = y³ ⇒ y³ = 1+ hence genral solution is y(t) = (1+)
Transcribed Image Text:Given equation y' + 7y= 2 we can write it as y2y' + 7y³ = 7 Let y³ = u and differentiate with respect to tboth sides we get 3y²y' = u' ⇒ y²y = qu' substitute it in equation u'+7u = 7 =u' + 21u = 21 = now this is linear and I. F = ef21dt - e21t Solution will be ux I. F = fI. Fx 7dt le²1t = 21 fe²¹tdt ue²1t e²¹t+C + C = ue²¹t = 21t 112³ + [ = n < replace u = y³ ⇒ y³ = 1+ hence genral solution is y(t) = (1+)
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