# Thread: First-order Nonlinear Equation with Linear Coefficients

1. ## First-order Nonlinear Equation with Linear Coefficients

How do I solve this one?

(2x - y + 4)dy + (x - 2y + 5)dx = 0

2. ## Re: First-order Nonlinear Equation with Linear Coefficients

Originally Posted by mafra
How do I solve this one?

(2x - y + 4)dy + (x - 2y + 5)dx = 0
Find the point of intersection of the two lines 2x - y + 4 = 0, and x - 2y + 5 = 0. Suppose that intersection occurs at the point $(x_{0},y_{0}).$ Then do the substitution $u=x-x_{0}$ and $v=y-y_{0}.$

The result of this substitution should result in a recognizeable type of DE. What do you get?