ODE
\[ y'(x)+2 \left (1-x \sqrt {y(x)}\right ) y(x)=0 \] ODE Classification
[_Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.248436 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \frac {1}{\left (x+c_1 e^x+1\right ){}^2}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 17
\[\left [\frac {1}{\sqrt {y \left (x \right )}}-x -1-{\mathrm e}^{x} \textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[2*(1 - x*Sqrt[y[x]])*y[x] + y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + x + E^x*C[1])^(-2)}}
Maple raw input
dsolve(diff(y(x),x)+2*y(x)*(1-x*y(x)^(1/2)) = 0, y(x))
Maple raw output
[1/y(x)^(1/2)-x-1-exp(x)*_C1 = 0]