What is the solution for (xy)^2y^'=(x+5)/(sqrt(y)) ?

The solution for (xy)^2y^'=(x+5)/(sqrt(y)) is y=((7xln(x)+7c_{1}x-35)/(2x))^{2/7}

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(xy)^2y^'=(x+5)/(sqrt(y))

(x y)^{2} y^{^{'}} = \frac{x + 5}{y}

y = (\frac{7 x ln ( x ) + 7 c _{1} x - 35}{2 x})^{\frac{2}{7}}

Solution steps

(x y)^{2} y^{'} (x) = \frac{x + 5}{y}

Solve separable ODE:

y = (\frac{7 x ln ( x ) + 7 c _{1} x - 35}{2 x})^{\frac{2}{7}}

y = (\frac{7 x ln ( x ) + 7 c _{1} x - 35}{2 x})^{\frac{2}{7}}

What is the solution for (xy)^2y^'=(x+5)/(sqrt(y)) ?
The solution for (xy)^2y^'=(x+5)/(sqrt(y)) is y=((7xln(x)+7c_{1}x-35)/(2x))^{2/7}