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}

\frac{d}{d x} (2 ln (2))

\int \frac{( x ^{2} - 25 ) ^{\frac{3}{2}}}{x ^{6}} d x

\frac{6 ( x ^{4} - 2 )}{x ^{3}}

(5 x^{2} + 8)^{8}

x - 1, 2, 5

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