4.6.28 \(x^2 y'(x)+x y(x)+\sqrt {y(x)}=0\)

ODE
\[ x^2 y'(x)+x y(x)+\sqrt {y(x)}=0 \] ODE Classification

[[_homogeneous, `class G`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0128784 (sec), leaf count = 21

\[\left \{\left \{y(x)\to \frac {\left (c_1 \sqrt {x}+1\right ){}^2}{x^2}\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 19

\[ \left \{ \sqrt {y \relax (x ) }-{x}^{-1}-{{\it \_C1}{\frac {1}{\sqrt {x}}}}=0 \right \} \] Mathematica raw input

DSolve[Sqrt[y[x]] + x*y[x] + x^2*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (1 + Sqrt[x]*C[1])^2/x^2}}

Maple raw input

dsolve(x^2*diff(y(x),x)+x*y(x)+y(x)^(1/2) = 0, y(x),'implicit')

Maple raw output

y(x)^(1/2)-1/x-1/x^(1/2)*_C1 = 0