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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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