What is the solution for y^'=(yx^2+x^2)^2 ?

The solution for y^'=(yx^2+x^2)^2 is y=-5/(x^5+5c_{1)}-(x^5)/(x^5+5c_{1)}-(5c_{1})/(x^5+5c_{1)}

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y^'=(yx^2+x^2)^2

y^{^{'}} = (y x^{2} + x^{2})^{2}

y = - \frac{5}{x ^{5} + 5 c _{1}} - \frac{x ^{5}}{x ^{5} + 5 c _{1}} - \frac{5 c _{1}}{x ^{5} + 5 c _{1}}

Solution steps

y^{'} (x) = (y x^{2} + x^{2})^{2}

Solve separable ODE:

y = - \frac{5}{x ^{5} + 5 c _{1}} - \frac{x ^{5}}{x ^{5} + 5 c _{1}} - \frac{5 c _{1}}{x ^{5} + 5 c _{1}}

y = - \frac{5}{x ^{5} + 5 c _{1}} - \frac{x ^{5}}{x ^{5} + 5 c _{1}} - \frac{5 c _{1}}{x ^{5} + 5 c _{1}}

y^{^{'}} - 3 y = 0, y (0) = 1

\frac{d y}{d x} = \frac{x ^{3}}{( y + 2 ) ^{2}}, y (0) = - 1

x^{^{'}} = 4 + 2 x

\frac{d y}{d x} = - k (y - 70), y (0) = 205

(1 + x^{2}) y^{^{'}} - x y = x y^{2}

What is the solution for y^'=(yx^2+x^2)^2 ?
The solution for y^'=(yx^2+x^2)^2 is y=-5/(x^5+5c_{1)}-(x^5)/(x^5+5c_{1)}-(5c_{1})/(x^5+5c_{1)}