What is the solution for (dx)/(dy)=(xy^3)/(sqrt(1+x^2)) ?

The solution for (dx)/(dy)=(xy^3)/(sqrt(1+x^2)) is

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(dx)/(dy)=(xy^3)/(sqrt(1+x^2))

\frac{d x}{d y} = \frac{x y ^{3}}{1 + x ^{2}}

y = 4 - 2 ln (x^{2} + 1 + 1) + 2 ln (x^{2} + 1 - 1) + 4 x^{2} + 1 + c_{1}, y = - 4 - 2 ln (x^{2} + 1 + 1) + 2 ln (x^{2} + 1 - 1) + 4 x^{2} + 1 + c_{1}

Solution steps

\frac{d}{d y} (x) = \frac{x y ^{3}}{1 + x ^{2}}

Solve separable ODE:

y = 4 - 2 ln (x^{2} + 1 + 1) + 2 ln (x^{2} + 1 - 1) + 4 x^{2} + 1 + c_{1}, y = - 4 - 2 ln (x^{2} + 1 + 1) + 2 ln (x^{2} + 1 - 1) + 4 x^{2} + 1 + c_{1}

y = 4 - 2 ln (x^{2} + 1 + 1) + 2 ln (x^{2} + 1 - 1) + 4 x^{2} + 1 + c_{1}, y = - 4 - 2 ln (x^{2} + 1 + 1) + 2 ln (x^{2} + 1 - 1) + 4 x^{2} + 1 + c_{1}

2 x - 6 y^{2} \frac{d y}{d x} + 4 = 0

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

(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

What is the solution for (dx)/(dy)=(xy^3)/(sqrt(1+x^2)) ?
The solution for (dx)/(dy)=(xy^3)/(sqrt(1+x^2)) is