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

The solution for (dy)/(dx)= x/(e^{-y)(1+x^2)^4} is y=-ln(1/(6(1+x^2)^3)-c_{1})

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(dy)/(dx)= x/(e^{-y)(1+x^2)^4}

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

y = - ln (\frac{1}{6 ( 1 + x ^{2} ) ^{3}} - c_{1})

Solution steps

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

Solve separable ODE:

y = - ln (\frac{1}{6 ( 1 + x ^{2} ) ^{3}} - c_{1})

y = - ln (\frac{1}{6 ( 1 + x ^{2} ) ^{3}} - c_{1})

(3 x^{2} + 2)^{2} y^{^{'}} - x y^{2} = 0, y (0) = \frac{3}{2}

\frac{x d x}{1 + x ^{2}} = \frac{d y}{y}

\frac{d y}{d x} = 2 x y, y (1) = 5

x^{^{'}} = 20 t - \frac{4 x}{30} t

2 x y \frac{d y}{d x} = 6 + 14 ln (x)

What is the solution for (dy)/(dx)= x/(e^{-y)(1+x^2)^4} ?
The solution for (dy)/(dx)= x/(e^{-y)(1+x^2)^4} is y=-ln(1/(6(1+x^2)^3)-c_{1})