What is the solution for (dy)/(dx)=xy^{1/2} ?

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

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(dy)/(dx)=xy^{1/2}

\frac{d y}{d x} = x y^{\frac{1}{2}}

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^{\frac{1}{2}}

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 \to - 3 lim (\frac{x ^{2} + 3}{4})

x \to 1 lim (e)

n = 1 \sum \infty (\frac{1}{3})^{k - n}

5 sec^{2} (x)

k = 1 \sum \infty \frac{x ^{k}}{k}

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