- #1
beetle2
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Homework Statement
[itex]y' = \frac{y+y^2}{x+x^2}[/itex]
Homework Equations
separation of variables
The Attempt at a Solution
I start with
[itex]y' = \frac{y+y^2}{x+x^2}[/itex]
which is
[itex]\frac{dy}{dx} = \frac{y+y^2}{x+x^2}[/itex]
next step is
[itex]dy = \frac{y+y^2}{x+x^2}dx[/itex]
than I divide both sides by [itex]y+y^2[/itex]
so gives
[itex]\frac{dy}{y+y^2} = \frac{1}{x+x^2}dx[/itex]
so then I integrate both sides.
[itex]\int\frac{dy}{y+y^2} = \int\frac{1}{x+x^2}dx[/itex]
which gives
[itex]ln\right[\frac{\mid y\mid}{\mid y+1\mid}\left][/itex]=[itex]ln\right[\frac{\mid x\mid}{\mid x+1\mid}\left][/itex]
Is this right so far?