ODE
\[ -x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
Change of variable
Mathematica ✗
cpu = 600.528 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.536 (sec), leaf count = 105
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2}=0,\ln \left ( x \right ) -{\it Artanh} \left ( {\frac {\sqrt {2}}{2}\sqrt {{\frac {{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}} \right ) +{\frac {1}{2}\ln \left ( {\frac {{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}} \right ) }-{\it \_C1}=0,\ln \left ( x \right ) +{\it Artanh} \left ( {\frac {\sqrt {2}}{2}\sqrt {{\frac {{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}} \right ) +{\frac {1}{2}\ln \left ( {\frac {{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}} \right ) }-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[-x^2 + 2*y[x]^2 - 2*x*y[x]*y'[x] + y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)-x^2+2*y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x)^2-x^2 = 0, ln(x)-arctanh(1/2*2^(1/2)*((x^2-y(x)^2)/x^2)^(1/2))+1/2*ln((x^2+y(x)^2)/x^2)-_C1 = 0, ln(x)+arctanh(1/2*2^(1/2)*((x^2-y(x)^2)/x^2)^(1/2))+1/2*ln((x^2+y(x)^2)/x^2)-_C1 = 0