I feel incredibly stupid for asking this. But which substitution can be used to obtain a general solution for

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

?

When I let v=(x+y)
I dead lock at dy/dx = (x-y)/(x+y)
It's clearly not homogeneous or of Bernoulli form. I'm probably blind to something here.

Question

I feel incredibly stupid for asking this. But which substitution can be used to obtain a general solution for

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

?

When I let v=(x+y)
I dead lock at dy/dx = (x-y)/(x+y)
It's clearly not homogeneous or of Bernoulli form. I'm probably blind to something here.

amistre64 · Answer

v = y/x i believe is the key

amistre64 · Answer

$$\frac{dy}{dx}  (x+y) = (x-y)$$
$$\frac{dy}{dx}= \frac{x-y}{x+y}$$
$$\frac{dy}{dx}= \frac{1-\frac{y}{x}}{1+\frac{y}{x}}$$
$$v=\frac{y}{x};\ y = vx$$
$$\frac{dy}{dx}=v$$
$$v= \frac{1-v}{1+v}$$

amistre64 · Answer

if i recall it correctly

amistre64 · Answer

does this look familiar?

anonymous · Answer

I just worked out the problem, but Yes. That was actually quite clever on dividing all the terms within the fraction by x. In the end it was homogeneous and I must eat my own words. Thank you.

amistre64 · Answer

:)  youre welcome, and good luck