thanks Solution This is a liner differential equation if is of the form dy/dx + f(x)y = g(x) then integrating factor is e^(integration of f(x) dx) hence from this equation you get integration factor of e^2x ^ sign means to the power Rest part is same as I did before e^2x is the integrating factor so we have y.e^2x = integration (8e^2x) on solving we get y.e^2x = 4e^(2x) + c y(0) = 0 so we get c = -4 y.e^2x = 4(e^2x - 1).