4.19.19 \(\left (1-x^2\right ) y'(x)^2+4 x^2+2 x y(x) y'(x)=0\)

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 = 0.349725 (sec), leaf count = 24

\[\left \{\left \{y(x)\to \frac {c_1^2-4 x^2+4}{2 c_1}\right \}\right \}\]

Maple
cpu = 0.292 (sec), leaf count = 31

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+4\,{x}^{2}-4=0,y \relax (x ) =-{\it \_C1}+{\it \_C1}\,{x}^{2}-{{\it \_C1}}^{-1} \right \} \] 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),'implicit')

Maple raw output

y(x)^2+4*x^2-4 = 0, y(x) = -_C1+_C1*x^2-1/_C1