Question

Find the general solution of these differential equations.

1) dy/dx = x/y² 2)dy/dx = x+2 / y

Answer 1

$1. \frac{dy}{dx} = \frac{x}{y^2}\\ \text{Cross-multiplying we have,}\\ y^2dy= (x+2)dx\\ \text{Integrating both sides we have}\\ \frac{y^3}{3}=\frac{x^2}{2}+c\\ 2. \frac{dy}{dx}=\frac{x+2}{y}\\ =ydy = (x+2)dx\\ =\frac{y^2}{2}=\frac{x^2}{2}+2x+c$