4.12.18 \(\left (1-x^2 y(x)\right ) y'(x)-x y(x)^2+1=0\)

ODE
\[ \left (1-x^2 y(x)\right ) y'(x)-x y(x)^2+1=0 \] ODE Classification

[_exact, _rational, [_Abel, `2nd type``class B`]]

Book solution method
Exact equation

Mathematica
cpu = 0.0104906 (sec), leaf count = 57

\[\left \{\left \{y(x)\to \frac {1-\sqrt {c_1 x^2+2 x^3+1}}{x^2}\right \},\left \{y(x)\to \frac {\sqrt {c_1 x^2+2 x^3+1}+1}{x^2}\right \}\right \}\]

Maple
cpu = 0.014 (sec), leaf count = 17

\[ \left \{ -{\frac {{x}^{2} \left (y \relax (x ) \right ) ^{2}}{2}}+x+y \relax (x ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[1 - x*y[x]^2 + (1 - x^2*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (1 - Sqrt[1 + 2*x^3 + x^2*C[1]])/x^2}, {y[x] -> (1 + Sqrt[1 + 2*x^3 + 
x^2*C[1]])/x^2}}

Maple raw input

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

Maple raw output

-1/2*x^2*y(x)^2+x+y(x)+_C1 = 0