What is the solution for y^'=x*sqrt(y) ?

The solution for y^'=x*sqrt(y) is y=(x^4}{16}+\frac{c_{1}x^2)/4+(c_{1}^2)/4

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y^'=x*sqrt(y)

y^{^{'}} = x \cdot y

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

Solution steps

y^{'} (x) = x \cdot 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}

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