Answer to Question #58204 in Differential Equations for Nayan Jyoti Das

Question

1. a) Solve the following ordinary differential equations:

i) 1/x sin ydx + [(ln x)(cos y) + y)] dy = 0

ii) d^2 y / dx^2 + dy/dx - 12y = 4e^2x

b) Solve the initial value problem:

d^2 y / dx^2 + 2(dy/dx) + 2y=0, y(0)=2, y'(0)=1