Answer to Question #244275 in Differential Equations for Jac

Question

Solve the differential equation of the following non-exact differential equation. Show complete solution.

(y - xy)dx + xdy = 0

Answer 1

$$xdy=y(x-1)dx$$

$$\dfrac{dy}{y}=\dfrac{x-1}{x}dx$$

Integrate

$$\int\dfrac{dy}{y}=\int\dfrac{x-1}{x}dx$$

$$\ln|y|=x-\ln|x|+\ln C$$

$$y=\dfrac{Ce^x}{x}$$