What is the solution for x^2*e^x+4*y*e^{(-y)}*y^'=0 ?

The solution for x^2*e^x+4*y*e^{(-y)}*y^'=0 is y=-\W((-e^xx^2+2e^xx-2e^x+c_{1})/(4e))-1

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x^2e^x+4ye^{(-y)}y^'=0

x^{2} \cdot e^{x} + 4 \cdot y \cdot e^{(- y)} \cdot y^{^{'}} = 0

y = - W (\frac{- e ^{x} x ^{2} + 2 e ^{x} x - 2 e ^{x} + c _{1}}{4 e}) - 1

Solution steps

x^{2} \cdot e^{x} + 4 \cdot y \cdot e^{(- y)} \cdot y^{'} (x) = 0

Solve separable ODE:

y = - W (\frac{- e ^{x} x ^{2} + 2 e ^{x} x - 2 e ^{x} + c _{1}}{4 e}) - 1

y = - W (\frac{- e ^{x} x ^{2} + 2 e ^{x} x - 2 e ^{x} + c _{1}}{4 e}) - 1

What is the solution for x^2*e^x+4*y*e^{(-y)}*y^'=0 ?
The solution for x^2*e^x+4*y*e^{(-y)}*y^'=0 is y=-\W((-e^xx^2+2e^xx-2e^x+c_{1})/(4e))-1