The solution of the differential equation $$ex2+ey2ydydx+ex2xy2$$−$$x=0$$ is

Correct option is 1ex2y2−1+ey2=c

Questions

$The solution of the differential equation (e^{x^{2}} + e^{y^{2}}) y \frac{d y}{d x} + e^{x^{2}} (x y^{2} - x) = 0 is$

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ex2y2−1+ey2=c

ey2x2−1+ex2=c

ey2y2−1+ex2=c

ex2y−1+ey2=c

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detailed solution

Correct option is A

Put y2=t⇒ex2eydtdx+2ex2(xt−x)=0ex2+et=2ex2x(t−1)dxdt=0 Put ex2=z⇒ex22xdxdy=dzdt∴z+et+dzdt(t−1)=0dzdt+zt−1=−ett−1 I. F=e∫dtt−1=t−1 G.S is ex2y2−1+ey2=c

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The solution of the differential equation ex2+ey2ydydx+ex2xy2−x=0 is

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$The solution of the differential equation (e^{x^{2}} + e^{y^{2}}) y \frac{d y}{d x} + e^{x^{2}} (x y^{2} - x) = 0 is$