Solving the Equation y^2- xy + (x+1)y' = 0

[psholtz]

Homework Statement

Solve the following equation:

$$y^2- xy + (x+1)y' = 0$$

The Attempt at a Solution

The equation isn't exact, and it isn't homogeneous.

I've tried a range of different substitutions, including v = y - x, v = y^2, v = y^2 - xy, none of which seem to lead down a fruitful path.

I've tried differentiating this expression, to obtain a second-order ODE, and then eliminate either the nonlinear term, or the y' term, etc, between the two expressions, but that doesn't seem to lead anywhere fruitful either..

Any hints? :-)

 

[jackmell]

Homework Statement

Solve the following equation:

$$y^2- xy + (x+1)y' = 0$$

The Attempt at a Solution

The equation isn't exact, and it isn't homogeneous.

I've tried a range of different substitutions, including v = y - x, v = y^2, v = y^2 - xy, none of which seem to lead down a fruitful path.

I've tried differentiating this expression, to obtain a second-order ODE, and then eliminate either the nonlinear term, or the y' term, etc, between the two expressions, but that doesn't seem to lead anywhere fruitful either..

Any hints? :-)

That' a Bernoulli equation. Put it in standard form and make the usual substitution. Check out any intro DE textbook for an example.