What is the solution for xdx+ye^{-x}dy=0,y^0=1 ?

The solution for xdx+ye^{-x}dy=0,y^0=1 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,y^0=1

x d x + y e^{- x} d y = 0, y^{0} = 1

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}

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