What is the solution for y^'=7sqrt(xy) ?

The solution for y^'=7sqrt(xy) is y=(49x^3)/9+(7c_{1}x^{3/2})/3+(c_{1}^2)/4

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y^'=7sqrt(xy)

y^{^{'}} = 7 x y

y = \frac{49 x ^{3}}{9} + \frac{7 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Solution steps

y^{'} (x) = 7 x y

Solve separable ODE:

y = \frac{49 x ^{3}}{9} + \frac{7 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y = \frac{49 x ^{3}}{9} + \frac{7 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

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

y^{^{'}} = \frac{x}{cos ( y )}, y (1) = 0

x - x^{2} d y - x y d x = 0

\frac{d y}{d x} = \frac{3 x y}{( ln ( y ) ) ^{4}}

y^{^{'}} = \frac{2 y}{5 x}

What is the solution for y^'=7sqrt(xy) ?
The solution for y^'=7sqrt(xy) is y=(49x^3)/9+(7c_{1}x^{3/2})/3+(c_{1}^2)/4