##### 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 = 0.362778 (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]