Question

solve the DE \[{dy \over dx} = -{1 \over x + y}\]

Answer 1

What is the latest method of differential equations are you learning?

Answer 2

Try substituting in v = x + y -> dv/dx = dy/dx + 1.

Answer 3

This becomes\[\frac{dv}{dx} - 1 = \frac{-1}{v}\]This is separable.

Answer 4

The original question was find the member of the orthogonal trajectories of the family of curves x + y = ce^x - 1 that passes through the point (3, 0). I think that I did the first part right

Answer 5

I got ln(v - 1) + v = x + c as an answer, with v = x + y.

Answer 6

Ahh I don't know why this is so hard!! Well it's a first order differential equation so you might want to look over that section.

Answer 7

\[\frac{dv}{dx} = \frac{v-1}{v} \rightarrow \int\limits \frac{v}{v-1}dv = \int\limits 1dx\]