What is the solution for xe^xln(y+1)dx+(x+1)^2(1/(y+1))dy=0 ?

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

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xe^xln(y+1)dx+(x+1)^2(1/(y+1))dy=0

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

y = e^{e^{\frac{e ^{x} x}{x + 1} - e^{x} + c_{1}}} - 1

Solution steps

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

Solve separable ODE:

y = e^{e^{\frac{e ^{x} x}{x + 1} - e^{x} + c_{1}}} - 1

y = e^{e^{\frac{e ^{x} x}{x + 1} - e^{x} + c_{1}}} - 1

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