What is the solution for (dx)/(dy)=(e^{-2y})/(x^2+4) ?

The solution for (dx)/(dy)=(e^{-2y})/(x^2+4) is y=-(ln(-(2x^3)/3-8x+c_{1}))/(2)

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(dx)/(dy)=(e^{-2y})/(x^2+4)

\frac{d x}{d y} = \frac{e ^{- 2 y}}{x ^{2} + 4}

y = - \frac{ln ( - \frac{2 x ^{3}}{3} - 8 x + c _{1} )}{2}

Solution steps

\frac{d}{d y} (x) = \frac{e ^{- 2 y}}{x ^{2} + 4}

Solve separable ODE:

y = - \frac{ln ( - \frac{2 x ^{3}}{3} - 8 x + c _{1} )}{2}

y = - \frac{ln ( - \frac{2 x ^{3}}{3} - 8 x + c _{1} )}{2}

\frac{d y}{d x} = \frac{x y}{ln ( y )}, y > 1

(2 y^{2} + 3 y) d x + 2 x y d y = 0

y^{^{'}} = \frac{cos ( x )}{2 y}, y (0) = - 1

(x^{3} + 5 x^{3} y^{4}) d x + e^{x^{4}} y^{3} d y = 0

\frac{d y}{d x} = - \frac{6}{9} x^{5} y^{9}

What is the solution for (dx)/(dy)=(e^{-2y})/(x^2+4) ?
The solution for (dx)/(dy)=(e^{-2y})/(x^2+4) is y=-(ln(-(2x^3)/3-8x+c_{1}))/(2)