What is the solution for y^'=6x^2*sqrt(y) ?

The solution for y^'=6x^2*sqrt(y) is y=x^6+c_{1}x^3+(c_{1}^2)/4

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y^'=6x^2*sqrt(y)

y^{^{'}} = 6 x^{2} \cdot y

y = x^{6} + c_{1} x^{3} + \frac{c _{1}^{2}}{4}

Solution steps

y^{'} (x) = 6 x^{2} \cdot y

Solve separable ODE:

y = x^{6} + c_{1} x^{3} + \frac{c _{1}^{2}}{4}

y = x^{6} + c_{1} x^{3} + \frac{c _{1}^{2}}{4}

\int 4 e^{- 7 x} d x

f (x) = \frac{x ^{3} + 5}{x}

e^{7 t}

\int_{\frac{1}{2}}^{1} (x^{- 3} - 21) d x

n = 0 \sum \infty \frac{1}{2 + 3 ^{n}}

What is the solution for y^'=6x^2*sqrt(y) ?
The solution for y^'=6x^2*sqrt(y) is y=x^6+c_{1}x^3+(c_{1}^2)/4