What is the solution for (dy)/(dx)=3x^2sqrt(y),y>0 ?

The solution for (dy)/(dx)=3x^2sqrt(y),y>0 is y=(x^6)/4+(c_{1}x^3)/2+(c_{1}^2)/4

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(dy)/(dx)=3x^2sqrt(y),y>0

\frac{d y}{d x} = 3 x^{2} y, y > 0

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{y + 9}{x + 8}

\frac{d y}{d t} + 20 y = 2, 4 = \frac{6}{5} - \frac{6}{5} e^{- 20 t}

y^{^{'}} = \frac{x y}{e ^{y}}, y (0) = 0

\frac{d P}{d t} = 0.15 P

\frac{d y}{d t} + 3 y = 2

What is the solution for (dy)/(dx)=3x^2sqrt(y),y>0 ?
The solution for (dy)/(dx)=3x^2sqrt(y),y>0 is y=(x^6)/4+(c_{1}x^3)/2+(c_{1}^2)/4