What is the solution for y^'=3sqrt(xy) ?

The solution for y^'=3sqrt(xy) is y=x^3+c_{1}x^{3/2}+(c_{1}^2)/4

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y^'=3sqrt(xy)

y^{^{'}} = 3 x y

y = x^{3} + c_{1} x^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

Solution steps

y^{'} (x) = 3 x y

Solve separable ODE:

y = x^{3} + c_{1} x^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

y = x^{3} + c_{1} x^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

\frac{7 + 2 x}{1 - 6 x}

\frac{x ^{2} - 6 x - 1}{( x - 3 ) ^{2}}

x \to 1 lim ([2 f (x) + g (x)])

\frac{\partial}{\partial x} (\frac{e ^{x} + e ^{y}}{2})

y = (\frac{( x + 2 )}{( x - 2 ) ^{2}})

What is the solution for y^'=3sqrt(xy) ?
The solution for y^'=3sqrt(xy) is y=x^3+c_{1}x^{3/2}+(c_{1}^2)/4