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

The solution for (dy)/(dx)=x^2sqrt(y),y>0 is y=(x^6}{36}+\frac{c_{1}x^3)/6+(c_{1}^2)/4

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

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

y = \frac{x ^{6}}{36} + \frac{c _{1} x ^{3}}{6} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{6}}{36} + \frac{c _{1} x ^{3}}{6} + \frac{c _{1}^{2}}{4}

y = \frac{x ^{6}}{36} + \frac{c _{1} x ^{3}}{6} + \frac{c _{1}^{2}}{4}

\frac{d y}{d x} = \frac{e ^{x} - cos ( 2 x )}{y}, y (0) = 2

(1 + 4 x) y ln (y) d x + (x + 2 x^{2}) d y = 0

y^{^{'}} = x e^{y - x^{2}}, y (0) = 0

t \frac{d y}{d t} = 15 y

y^{^{'}} + 2 x y = x, y (0) = 2

What is the solution for (dy)/(dx)=x^2sqrt(y),y>0 ?
The solution for (dy)/(dx)=x^2sqrt(y),y>0 is y=(x^6}{36}+\frac{c_{1}x^3)/6+(c_{1}^2)/4