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

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

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

\frac{d y}{d x} = (x y)

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

Solution steps

\frac{d y}{d x} = (x y)

Solve separable ODE:

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

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

(x + 1) y^{^{'}} + y^{2} = 0

\frac{d x}{d t} + \frac{x}{100} = 75

(x^{2} - 3) \frac{d y}{d x} = x (y^{2} + 16), y (2) = 4

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

y^{^{'}} = \frac{4 x}{1 + 2 y}, y (9) = 0

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