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#### find_the_fun

##### Active member

- Feb 1, 2012

- 166

For the D.E. \(\displaystyle (x-y^3+y^2 \sin{x})dx = (3xy^2+2y \cos{x}) dy\) is the solution \(\displaystyle xy^3+\frac{x^2}{2}+y^2 \cos{x}=c\) ? That's what I got but the back of book said \(\displaystyle \frac{x^2}{2}\) should negative, not positive. How does this happen? I get \(\displaystyle \frac{x^2}{2}\) from integrating x so where does the negative come from?

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