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10. (a) Let fi be a solution of dy dx + P(x)y = Q1(x), and f2 be a solution of dy + P(x)y = Q2(x), da where P, Q1, and Q2 are all defined on the same real interval I. Prove that fi + f2 is a solution of dy da + P(x)y = Q1(x)+Q2(x) on I. (b) Use the result of (a) to solve the equation dy +y = 2 sin x + 5 sin 2x. dx

10. (a) Let fi be a solution of dy dx + P(x)y = Q1(x), and f2 be a solution of dy + P(x)y = Q2(x), da where P, Q1, and Q2 are all defined on the same real interval I. Prove that fi + f2 is a solution of dy da + P(x)y = Q1(x)+Q2(x) on I. (b) Use the result of (a) to solve the equation dy +y = 2 sin x + 5 sin 2x. dx

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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10. Solve the IVP

10. (a) Let fi be a solution of dy dx + P(x)y = Q1(x), and f2 be a solution of dy + P(x)y = Q2(x), da where P, Q1, and Q2 are all defined on the same real interval I. Prove that fi + f2 is a solution of dy da + P(x)y = Q1(x)+Q2(x) on I. (b) Use the result of (a) to solve the equation dy +y = 2 sin x + 5 sin 2x. dx
Transcribed Image Text:10. (a) Let fi be a solution of dy dx + P(x)y = Q1(x), and f2 be a solution of dy + P(x)y = Q2(x), da where P, Q1, and Q2 are all defined on the same real interval I. Prove that fi + f2 is a solution of dy da + P(x)y = Q1(x)+Q2(x) on I. (b) Use the result of (a) to solve the equation dy +y = 2 sin x + 5 sin 2x. dx
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