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 = 0.362778 (sec), leaf count = 57
\[\left \{\left \{y(x)\to \frac {1-\sqrt {2 x^3+c_1 x^2+1}}{x^2}\right \},\left \{y(x)\to \frac {1+\sqrt {2 x^3+c_1 x^2+1}}{x^2}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 50
\[\left [y \left (x \right ) = \frac {1+\sqrt {2 x^{2} \textit {\_C1} +2 x^{3}+1}}{x^{2}}, y \left (x \right ) = -\frac {-1+\sqrt {2 x^{2} \textit {\_C1} +2 x^{3}+1}}{x^{2}}\right ]\] 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))
Maple raw output
[y(x) = (1+(2*_C1*x^2+2*x^3+1)^(1/2))/x^2, y(x) = -(-1+(2*_C1*x^2+2*x^3+1)^(1/2))/x^2]