What is the solution for (1+e^xy+xe^xy)dx+(xe^x+2)dy=0 ?

The solution for (1+e^xy+xe^xy)dx+(xe^x+2)dy=0 is y=(c_{1})/(2+xe^x)-x/(2+xe^x)

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(1+e^xy+xe^xy)dx+(xe^x+2)dy=0

(1 + e^{x} y + x e^{x} y) d x + (x e^{x} + 2) d y = 0

y = \frac{c _{1}}{2 + x e ^{x}} - \frac{x}{2 + x e ^{x}}

Solution steps

(1 + e^{x} y + x e^{x} y) d x + (x e^{x} + 2) d y = 0

Solve exact ODE:

y = \frac{c _{1}}{2 + x e ^{x}} - \frac{x}{2 + x e ^{x}}

y = \frac{c _{1}}{2 + x e ^{x}} - \frac{x}{2 + x e ^{x}}

\int \frac{9 x ^{3} - 5 x ^{2} + 3 x}{x} d x

e^{0.04 t}

x \to - 3 lim (\frac{x ^{2} - 9}{x - 3})

x \to 0 lim ([\frac{sin ( x )}{x}])

\frac{d y}{d x} = y^{- 2}

What is the solution for (1+e^xy+xe^xy)dx+(xe^x+2)dy=0 ?
The solution for (1+e^xy+xe^xy)dx+(xe^x+2)dy=0 is y=(c_{1})/(2+xe^x)-x/(2+xe^x)