What is the solution for y^'=(6yx^2)/(x^3+1) ?

The solution for y^'=(6yx^2)/(x^3+1) is y=e^{c_{1}}x^6+2e^{c_{1}}x^3+e^{c_{1}}

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y^'=(6yx^2)/(x^3+1)

y^{^{'}} = \frac{6 y x ^{2}}{x ^{3} + 1}

y = e^{c_{1}} x^{6} + 2 e^{c_{1}} x^{3} + e^{c_{1}}

Solution steps

y^{'} (x) = \frac{6 y x ^{2}}{x ^{3} + 1}

Solve separable ODE:

y = e^{c_{1}} x^{6} + 2 e^{c_{1}} x^{3} + e^{c_{1}}

y = e^{c_{1}} x^{6} + 2 e^{c_{1}} x^{3} + e^{c_{1}}

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

\frac{d y}{d x} = \frac{6 y}{x}, x > 0

y^{^{'}} = 3 \frac{y}{x - 1}

y^{^{'}} + 6 y = 4, y (0) = 0

x \frac{d y}{d x} = y x - x y cos (x), y = 1, x = 0

What is the solution for y^'=(6yx^2)/(x^3+1) ?
The solution for y^'=(6yx^2)/(x^3+1) is y=e^{c_{1}}x^6+2e^{c_{1}}x^3+e^{c_{1}}