What is the solution for (dy)/(dx)=6x^3sqrt(y),y>0 ?

The solution for (dy)/(dx)=6x^3sqrt(y),y>0 is y=(9x^8}{16}+\frac{3c_{1}x^4)/4+(c_{1}^2)/4

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(dy)/(dx)=6x^3sqrt(y),y>0

\frac{d y}{d x} = 6 x^{3} y, y > 0

y = \frac{9 x ^{8}}{16} + \frac{3 c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 6 x^{3} y

Solve separable ODE:

y = \frac{9 x ^{8}}{16} + \frac{3 c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{9 x ^{8}}{16} + \frac{3 c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

\frac{d y}{d t} = \frac{9 t ^{2}}{5 y}

(x - 4) (x + 4) y^{^{'}} - x y^{2} = 0

x \frac{d y}{d x} + 3 y = 0

\frac{d y}{d x} = 90 y x^{9}

x^{3} y + 7 x^{2} y^{^{'}} + 6 y = 0

What is the solution for (dy)/(dx)=6x^3sqrt(y),y>0 ?
The solution for (dy)/(dx)=6x^3sqrt(y),y>0 is y=(9x^8}{16}+\frac{3c_{1}x^4)/4+(c_{1}^2)/4