What is the particular solution to the differential equation....

Question

What is the particular solution to the differential equation dy/dx= (1-y)^2/e^2x with the initial condition y(0)=-5?

Answer 1

We separate variables and integrate: ∫(1 - y)^-2dy = ∫e^-2xdx;

(y-1)^-1/(-1) = -1/2 e^-2x + C; -1/(y - 1) = -1/2e^{- 2x} + C; y(0) = - 5; - 1/(-6) = - 1/2 + C; C = 1/2 + 1/6 = 2/3

1/(1 - y) = - 1/2e^-2x + 2/3

Answer 2

y=(-3*exp(-2x)-2)/(4-3*exp(-2x))