4.3.3 \(y'(x)+2 \left (1-x \sqrt {y(x)}\right ) y(x)=0\)

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 = 0.018551 (sec), leaf count = 16

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

Maple
cpu = 0.008 (sec), leaf count = 17

\[ \left \{ {\frac {1}{\sqrt {y \relax (x ) }}}-x-1-{{\rm e}^{x}}{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)^(1/2)-x-1-exp(x)*_C1 = 0