It is a differential equation question. Please solve step by step 1) (a) Let fi be a solution ofdy+ P(x)y = Q1(x)dxand f2 be a solution ofdy+ P(x)y = Q2(x),dxwhere P, Q1, and Q2 are all defined on the same real interval I. Prove that fi + f2 is a solution ofdy+ P(г)у — Q1() + Qz(х)dxon I.(b) Use the result of (a) to solve the equationdy+ y = 2 sin x+5 sin 2x.dx

let y1x=f1x and y2x=f2xdy1dx=f1'(x) and dy2dx=f2'(x) Since y1x=f1x and y2x=f2x are the solution of…

1) (a) Let fi be a solution of dy + P(x)y= Q1(x) dx %3D and f2 be a solution of dy + P(x)y = Q2(x), dr where P, Q1, and Q2 are all defined on the same real interval I. Prove that fi+ f2 is a solution of dy + P(x)y= Q1(x)+Q2(x) dx %3D on I. (b) Use the result of (a) to solve the equation dy ·+ y = 2 sin x+5 sin 2x. dx

1) (a) Let fi be a solution of dy + P(x)y= Q1(x) dx %3D and f2 be a solution of dy + P(x)y = Q2(x), dr where P, Q1, and Q2 are all defined on the same real interval I. Prove that fi+ f2 is a solution of dy + P(x)y= Q1(x)+Q2(x) dx %3D on I. (b) Use the result of (a) to solve the equation dy ·+ y = 2 sin x+5 sin 2x. dx

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

It is a differential equation question. Please solve step by step

1) (a) Let fi be a solution of
dy
+ P(x)y = Q1(x)
dx
and f2 be a solution of
dy
+ P(x)y = Q2(x),
dx
where P, Q1, and Q2 are all defined on the same real interval I. Prove that fi + f2 is a solution of
dy
+ P(г)у — Q1() + Qz(х)
dx
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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