Differential Equation Method Question

[jofree87]

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

 

[Gib Z]

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.

 

[Sweet_GirL]

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 $$v=x+y$$.