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olve the following linear inhomogeneous equations using integrating factors. For each question you need to enter: The function u(x) The function v(x), including the integrating constant C The general solution y(x) without the given condition applied The general solution after applying the given condition y' - 2y = xe* with y(0) = 1 (x) = e -2x 2x (x) = -xe* e²x dx + C (x) = -xẻ -ẽ +C-e

olve the following linear inhomogeneous equations using integrating factors. For each question you need to enter: The function u(x) The function v(x), including the integrating constant C The general solution y(x) without the given condition applied The general solution after applying the given condition y' - 2y = xe* with y(0) = 1 (x) = e -2x 2x (x) = -xe* e²x dx + C (x) = -xẻ -ẽ +C-e

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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Solve the following linear inhomogeneous equations using integrating factors. For each question you need to enter: The function u(x) The function v(x), including the integrating constant C The general solution y(x) without the given condition applied The general solution after applying the given condition a. y' - 2y = xe* with y(0) = 1 u (x) = v (x) = -xe* - e²x dx + C y (x) = -xet - et +C-e²x -2x y (x) = -xet - et + 2e²x b. y' + 2xy = x3 with y(0) = 1 U (x) = v (x) = y (x) = X (x² − 1) + C² e ²¹² 3 y (x) = 1/²(x²-1) + 2²/e-x²
Transcribed Image Text:Solve the following linear inhomogeneous equations using integrating factors. For each question you need to enter: The function u(x) The function v(x), including the integrating constant C The general solution y(x) without the given condition applied The general solution after applying the given condition a. y' - 2y = xe* with y(0) = 1 u (x) = v (x) = -xe* - e²x dx + C y (x) = -xet - et +C-e²x -2x y (x) = -xet - et + 2e²x b. y' + 2xy = x3 with y(0) = 1 U (x) = v (x) = y (x) = X (x² − 1) + C² e ²¹² 3 y (x) = 1/²(x²-1) + 2²/e-x²
c. xy' = x cos x - 2 sin x - 2y with y(π) = 0 U (x) = v (x) = y (x) = sin(x) + y (x) = sin(x) + u (x) = d. xy' = 2x² + y with y(1) = 2 v (x) = -1 y (x) = x³ + C-x 4 cos(x) y (x) = x² + x x³+x 4 cos(x) 4 sin(x) 4 sin(x) x² بان
Transcribed Image Text:c. xy' = x cos x - 2 sin x - 2y with y(π) = 0 U (x) = v (x) = y (x) = sin(x) + y (x) = sin(x) + u (x) = d. xy' = 2x² + y with y(1) = 2 v (x) = -1 y (x) = x³ + C-x 4 cos(x) y (x) = x² + x x³+x 4 cos(x) 4 sin(x) 4 sin(x) x² بان
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