Problem with a Diff Equation

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January 31st 2007, 10:51 PM
machi4velli

Problem with a Diff Equation

I am having problems solving this differential equation:

(dy/dx) = (x + y)^2

Any help would be appreciated.
February 1st 2007, 05:15 AM
ThePerfectHacker

Quote:

Originally Posted by machi4velli

I am having problems solving this differential equation:

(dy/dx) = (x + y)^2

Any help would be appreciated.

We have,
$y'=(x+y)^2$
Define a new function,
$z=x+y$ .
Then,
$z'=1+y'\to y'=z'-1$
Thus,
$z'-1=z^2$
$z'=1+z^2$
$\frac{z'}{1+z^2}=1$
$\int \frac{z'}{1+z^2} dx=\int 1 dx$
$\tan^{-1} z=x+C$
$\tan^{-1} (x+y)=x+C$
Are all the solutions on some non-zero open interval.

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