What is the solution for xdx+ye^{-x}dy=0 ?

The solution for xdx+ye^{-x}dy=0 is y=sqrt(-2e^xx+2e^x+c_{1)},y=-sqrt(-2e^xx+2e^x+c_{1)}

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xdx+ye^{-x}dy=0

x d x + y e^{- x} d y = 0

y = - 2 e^{x} x + 2 e^{x} + c_{1}, y = - - 2 e^{x} x + 2 e^{x} + c_{1}

Solution steps

x d x + y e^{- x} d y = 0

Solve separable ODE:

y = - 2 e^{x} x + 2 e^{x} + c_{1}, y = - - 2 e^{x} x + 2 e^{x} + c_{1}

y = - 2 e^{x} x + 2 e^{x} + c_{1}, y = - - 2 e^{x} x + 2 e^{x} + c_{1}

\int (\frac{x ^{2}}{9 - x ^{2}}) d x

\frac{d}{d x} (\frac{( 2 x ^{3} + a x + a )}{x ^{2} - 1})

\int 4 x^{2} e^{x^{3}} d x

y = - 2 x^{3} + \frac{6}{x}, at x = - 1

\int \frac{x ^{3}}{2 x ^{4} + x ^{2} - 1} d x

What is the solution for xdx+ye^{-x}dy=0 ?
The solution for xdx+ye^{-x}dy=0 is y=sqrt(-2e^xx+2e^x+c_{1)},y=-sqrt(-2e^xx+2e^x+c_{1)}