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

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

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xy^'=y+2sqrt(xy)

x y^{^{'}} = y + 2 x y

y = x ln^{2} (x) + 2 c_{1} x ln (x) + c_{1}^{2} x

Solution steps

x y^{'} (x) = y + 2 x y

Solve Bernoulli ODE:

y = x ln^{2} (x) + 2 c_{1} x ln (x) + c_{1}^{2} x

y = x ln^{2} (x) + 2 c_{1} x ln (x) + c_{1}^{2} x

(1 + x)^{2}

\int (x - 1)^{2} (1 + x^{\frac{1}{2}})^{2} d x

arctan (16 x)

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

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