# Differential Equation Method Question

dy/dx = (y-x)/(y+x)

I am suppose to solve this equation using substitution, but isn't it possible to solve this equation an easier way since it is an exact equation?

(y+x)dy - (y-x)dx = 0

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Gib Z
Homework Helper
It's not an exact ODE. The form is $$P(x,y)dy + Q(x,y) dx = 0$$ for exact ODE's, you didn't bring the negative factor in.

dy/dx = (y-x)/(y+x)

I am suppose to solve this equation using substitution, but isn't it possible to solve this equation an easier way since it is an exact equation?

(y+x)dy - (y-x)dx = 0
$$\frac{dy}{dx}=\frac{y-x}{y+x}=\frac{y}{y+x}-\frac{x}{y+x}$$

Use the substitution $$v=x+y$$.