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 = 0.255851 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {\left (1+c_1 \sqrt {x}\right ){}^2}{x^2}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 19
\[\left [\sqrt {y \left (x \right )}-\frac {1}{x}-\frac {\textit {\_C1}}{\sqrt {x}} = 0\right ]\] 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))
Maple raw output
[y(x)^(1/2)-1/x-1/x^(1/2)*_C1 = 0]