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7. (a) Use the method of variation of parameters to show that the solution of +k²y = o(r) satisfying the initial conditions y(0) = 0, y'(0) = 0 is dr² y(x) = o(t) sink(z - t)dt. (b) solve the system of differential equations dt +(x+2y) = 1 + 2(x - y) = t

7. (a) Use the method of variation of parameters to show that the solution of +k²y = o(r) satisfying the initial conditions y(0) = 0, y'(0) = 0 is dr² y(x) = o(t) sink(z - t)dt. (b) solve the system of differential equations dt +(x+2y) = 1 + 2(x - 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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7. (a) Use the method of variation of parameters to show that the solution of d'y +k²y = o(a) satisfying the initial conditions y(0) = 0, y'(0) = 0 is dr² y(x) = (t) sink (x-1)dt. (b) solve the system of differential equations dz dt dy dt + (x+2y) = 1 +2(z-y) = t
Transcribed Image Text:7. (a) Use the method of variation of parameters to show that the solution of d'y +k²y = o(a) satisfying the initial conditions y(0) = 0, y'(0) = 0 is dr² y(x) = (t) sink (x-1)dt. (b) solve the system of differential equations dz dt dy dt + (x+2y) = 1 +2(z-y) = t
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