Simple differential equation

  • #1
CalculusHelp1
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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?
 

Answers and Replies

  • #2
micromass
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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?
 
  • #3
CalculusHelp1
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Thanks again micromass
 
  • #4
Liquidxlax
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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
 
  • #5
CalculusHelp1
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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.
 

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