ODE
\[ \left (1-x^2\right ) y'(x)^2+4 x^2+2 x y(x) y'(x)=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 0.460273 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {-4 x^2+4+c_1{}^2}{2 c_1}\right \}\right \}\]
Maple ✓
cpu = 1.697 (sec), leaf count = 46
\[\left [y \left (x \right ) = -2 \sqrt {-x^{2}+1}, y \left (x \right ) = 2 \sqrt {-x^{2}+1}, y \left (x \right ) = -\textit {\_C1} +x^{2} \textit {\_C1} -\frac {1}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[4*x^2 + 2*x*y[x]*y'[x] + (1 - x^2)*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (4 - 4*x^2 + C[1]^2)/(2*C[1])}}
Maple raw input
dsolve((-x^2+1)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+4*x^2 = 0, y(x))
Maple raw output
[y(x) = -2*(-x^2+1)^(1/2), y(x) = 2*(-x^2+1)^(1/2), y(x) = -_C1+x^2*_C1-1/_C1]