Check whether the differential equation: Is Exact or not? If yes, $$ \frac{ ext { find }}{\left(6 x^{2}+4 x y+y^{2} ight) d x+\left(2 x^{2}+2 x y-3 y^{2} ight) d y=0} $$.

Question

Check whether the differential equation: Is Exact or not? If yes, $$ \frac{	ext { find }}{\left(6 x^{2}+4 x y+y^{2}ight) d x+\left(2 x^{2}+2 x y-3 y^{2}ight) d y=0} $$.

Thornton Simpson · Accepted Answer

The differential equation is exact, and its general solution is: $$ 2x^{3} + 2x^{2}y + x y^{2} - y^{3} = C $$ where $$ C $$ is a constant.

Check whether the differential equation: Is Exact or not? If yes, \( \frac{\text { find }}{\left(6 x^{2}+4 x y+y^{2}\right) d x+\left(2 x^{2}+2 x y-3 y^{2}\right) d y=0} \).

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Check whether the differential equation: Is Exact or not? If yes, \( \frac{\text { find }}{\left(6 x^{2}+4 x y+y^{2}\right) d x+\left(2 x^{2}+2 x y-3 y^{2}\right) d y=0} \).

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