What is the solution for (dy)/(dx)=9xsqrt(y) ?

The solution for (dy)/(dx)=9xsqrt(y) is y=(81x^4}{16}+\frac{9c_{1}x^2)/4+(c_{1}^2)/4

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(dy)/(dx)=9xsqrt(y)

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

y = \frac{81 x ^{4}}{16} + \frac{9 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{81 x ^{4}}{16} + \frac{9 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{81 x ^{4}}{16} + \frac{9 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

\int x (x - 2) d x

4 \frac{d ^{2} y}{d x ^{2}} - 5 y = 0

x \to 4 lim (\frac{sin ( x )}{x})

\frac{d y}{d x}, y e^{y} \cdot \frac{x - 1}{x + 1} = \frac{x ^{3}}{3} - x

\int_{0}^{8} x d x

What is the solution for (dy)/(dx)=9xsqrt(y) ?
The solution for (dy)/(dx)=9xsqrt(y) is y=(81x^4}{16}+\frac{9c_{1}x^2)/4+(c_{1}^2)/4