What is the solution for y^'=(xy^3)/4 ?

The solution for y^'=(xy^3)/4 is y=sqrt(-4/(x^2+c_{1))},y=-sqrt(-4/(x^2+c_{1))}

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y^'=(xy^3)/4

y^{^{'}} = \frac{x y ^{3}}{4}

y = - \frac{4}{x ^{2} + c _{1}}, y = - - \frac{4}{x ^{2} + c _{1}}

Solution steps

y^{'} (x) = \frac{x y ^{3}}{4}

Solve separable ODE:

y = - \frac{4}{x ^{2} + c _{1}}, y = - - \frac{4}{x ^{2} + c _{1}}

y = - \frac{4}{x ^{2} + c _{1}}, y = - - \frac{4}{x ^{2} + c _{1}}

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

\frac{d y}{d x} y = \frac{1}{x ^{10}}

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

y^{^{'}} = y^{2} - 4

y^{^{'}} = y^{2} - 20 y + 100

What is the solution for y^'=(xy^3)/4 ?
The solution for y^'=(xy^3)/4 is y=sqrt(-4/(x^2+c_{1))},y=-sqrt(-4/(x^2+c_{1))}