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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 20EQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65e8876c-9cfb-4d00-b5f3-6286bfdc9996%2F074f7a0b-dfd9-4f73-888d-85ec5d0b1a58%2Fvj9mptl_processed.png&w=3840&q=75)
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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