- #1
KillerZ
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Homework Statement
Solve the given differential equation by separation of variables.
Homework Equations
[tex]\frac{dy}{dx} = \frac{xy + 2y - x - 2}{xy - 3y + x - 3}[/tex]
The Attempt at a Solution
[tex]\frac{dy}{dx} = \frac{xy + 2y - x - 2}{xy - 3y + x - 3}[/tex]
[tex] = \frac{(x + 2)(y - 1)}{(x - 3)(y + 1)}[/tex]
[tex](x - 3)(y + 1)\frac{dy}{dx} = (x + 2)(y - 1)[/tex]
[tex]\frac{(x - 3)(y + 1)}{(y - 1}\frac{dy}{dx} = (x + 2)[/tex]
[tex]\frac{(y + 1)}{(y - 1)}\frac{dy}{dx} = \frac{(x + 2)}{(x - 3)}[/tex]
[tex]\frac{(y + 1)}{(y - 1)}dy = \frac{(x + 2)}{(x - 3)}dx[/tex]
This is where I am having problems I am not sure what way to Integrate this:
[tex]\int\frac{(y + 1)}{(y - 1)}dy = \int\frac{(x + 2)}{(x - 3)}dx[/tex]
I though maybe by partial fractions but the degree of the numerator is not less than the degree of the denominator.