Question

(1+Xsquared+ysquared+xsquaredtimesysquared)dy=ysquareddx
My mind is blank. I can't even figure out how to start this.

Answer 1

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Answer 2

So you have:
\[\int\limits 1+x^2+y^2+xy^2 dy=\int\limits y^2 dx?\].
Or:
\[(1+x^2+y^2+xy^2)dy=y^2 dx\].?

Answer 3

Or some other form?

Answer 4

the second one

Answer 5

xysquared should be xsquaredysquared

Answer 6

Well 1+x^2+y^2+x^2y^2=(x^2+1)(y^2+1)
So:
(y^2+1)/y^2 dy=dx/(x^2+1)
Integrating:
\[\int\limits \frac{y^2+1}{y^2}=\int\limits \frac{dx}{x^2+1}\]
\[\int\limits 1+y^{-2} dy=\int\limits \frac{dx}{x^2+1}\]
\[y-y^{-1}=\arctan(x)\]
Factoring out a y^(-1):
\[\frac{y^2-1}{y}=\arctan(x)\].