Answer to Question #223118 in Complex Analysis for Basy

Question

Find the general solution of each differential equation, expressing y explicitly in terms of x.

5) dy/dx = x(y+1)

Answer 1

$$dy/dx=x(y+1)$$

$$\dfrac{dy}{y+1}=xdx$$

Integrate

$$\int \dfrac{dy}{y+1}=\int xdx$$

$$\ln |y+1|=\dfrac{x^2}{2}+\ln C$$

$$y=Ce^{(x^2/2)}-1$$