ODE
\[ 9 \left (1-x^2\right ) y(x)^4 y'(x)^2+4 x^2+6 x y(x)^5 y'(x)=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
Book solution method
Change of variable
Mathematica ✗
cpu = 616.913 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 2.7 (sec), leaf count = 62
\[ \left \{ -{\it \_C1}- \left ( y \left ( x \right ) \right ) ^{3}+\sqrt { \left ( y \left ( x \right ) \right ) ^{6}+4\,{x}^{2}-4}=0,-{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{3}+\sqrt { \left ( y \left ( x \right ) \right ) ^{6}+4\,{x}^{2}-4}=0, \left ( y \left ( x \right ) \right ) ^{6}+4\,{x}^{2}-4=0 \right \} \] Mathematica raw input
DSolve[4*x^2 + 6*x*y[x]^5*y'[x] + 9*(1 - x^2)*y[x]^4*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(9*(-x^2+1)*y(x)^4*diff(y(x),x)^2+6*x*y(x)^5*diff(y(x),x)+4*x^2 = 0, y(x),'implicit')
Maple raw output
y(x)^6+4*x^2-4 = 0, -_C1+y(x)^3+(y(x)^6+4*x^2-4)^(1/2) = 0, -_C1-y(x)^3+(y(x)^6+4*x^2-4)^(1/2) = 0