Problem 7: Consider the differential equation x²y" – 2xy' + (x² + 2)y = 0, x > 0 You are given that y1 = x cos(x) is a solution to this differential equa- tion. (a) Find the general solution to the differential equation. (b) Solve the initial value problem given by x²y" – 2xy' + (x² + 2)y = x°, y(T) = y'(T) = 0

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 differentia…