Integrating Functions with Variables: Solving Differential Equations

[CalculusHelp1]

Homework Statement

f'(x)= x+1-yx-y

Solve for f(x)

Homework Equations

definitions of integrals and derivatives

The Attempt at a Solution

Okay, so I integrated both sides.

This gives f(x) = x^2/2 + x -integral(yx) - integral(y) +c

The problem I'm having is how do you integrate when there is a y in the function? I'm guessing this has something to do with the definition, i.e. f(x)=y=integral(f'(x)), I'm just not sure how to manipulate the equation. Does anyone know the trick to this?

 

[micromass]

So you've got the equation y'=x+1-yx-y. This is a separable ODE, you can write it as y'=(x+1)-y(x+1). Thus y'/(1-y)=x+1.
Can you solve it now?

 

[CalculusHelp1]

Thanks again micromass

 

[Liquidxlax]

So you've got the equation y'=x+1-yx-y. This is a separable ODE, you can write it as y'=(x+1)-y(x+1). Thus y'/(1-y)=x+1.
Can you solve it now?

ummm but he stated f(x), not a function of y. Unless I'm mistaken

 

[CalculusHelp1]

Sorry i was given dy/dx and was asked to solve for y, i just replaced with with f(x) and dy/dx with f'(x). The solution was to separate the variables, I forgot all about it.