What is the solution for (dx)/(dy(sqrt(y)))=e^{-x} ?

The solution for (dx)/(dy(sqrt(y)))=e^{-x} is y=\sqrt[3]{(9e^{2x}+9c_{1}^2+18c_{1}e^x)/4}

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(dx)/(dy(sqrt(y)))=e^{-x}

\frac{d x}{d y ( y )} = e^{- x}

y = 3 \frac{9 e ^{2 x} + 9 c _{1}^{2} + 18 c _{1} e ^{x}}{4}

Solution steps

\frac{d x}{d y ( y )} = e^{- x}

Solve separable ODE:

y = 3 \frac{9 e ^{2 x} + 9 c _{1}^{2} + 18 c _{1} e ^{x}}{4}

y = 3 \frac{9 e ^{2 x} + 9 c _{1}^{2} + 18 c _{1} e ^{x}}{4}

y^{^{'}} + 2 y = 2, 6 e^{- t} y (0) = 3

y^{^{'}} y^{2} = x^{2}

\frac{d y}{d x} = (2 x) (sec (y))

x^{2} y + y^{^{'}} = 3 x^{2}

y^{^{'}} = - 6 y + 12

What is the solution for (dx)/(dy(sqrt(y)))=e^{-x} ?
The solution for (dx)/(dy(sqrt(y)))=e^{-x} is y=\sqrt[3]{(9e^{2x}+9c_{1}^2+18c_{1}e^x)/4}