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

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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.