ODE
\[ \text {f0} y''(x)^2+\text {f1} y'(x) y''(x)+\text {f2} y(x) y''(x)+\text {g0} y'(x)^2+\text {g1} y(x) y'(x)+h y(x)^2=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 600.078 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 2.148 (sec), leaf count = 148
\[ \left \{ \ln \left ( y \left ( x \right ) \right ) -\int \!{\it RootOf} \left ( x-2\,\int ^{{\it \_Z}}\!{\frac {{\it f0}}{-2\,{\it f0}\,{{\it \_f}}^{2}-{\it \_f}\,{\it f1}+\sqrt {-4\,{{\it \_f}}^{2}{\it f0}\,{\it g0}+{{\it \_f}}^{2}{{\it f1}}^{2}-4\,{\it \_f}\,{\it f0}\,{\it g1}+2\,{\it \_f}\,{\it f1}\,{\it f2}-4\,{\it f0}\,h+{{\it f2}}^{2}}-{\it f2}}}{d{\it \_f}}+{\it \_C1} \right ) \,{\rm d}x-{\it \_C2}=0,\ln \left ( y \left ( x \right ) \right ) -\int \!{\it RootOf} \left ( x+2\,\int ^{{\it \_Z}}\!{\frac {{\it f0}}{2\,{\it f0}\,{{\it \_f}}^{2}+{\it \_f}\,{\it f1}+\sqrt {-4\,{{\it \_f}}^{2}{\it f0}\,{\it g0}+{{\it \_f}}^{2}{{\it f1}}^{2}-4\,{\it \_f}\,{\it f0}\,{\it g1}+2\,{\it \_f}\,{\it f1}\,{\it f2}-4\,{\it f0}\,h+{{\it f2}}^{2}}+{\it f2}}}{d{\it \_f}}+{\it \_C1} \right ) \,{\rm d}x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[h*y[x]^2 + g1*y[x]*y'[x] + g0*y'[x]^2 + f2*y[x]*y''[x] + f1*y'[x]*y''[x] + f0*y''[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(f0*diff(diff(y(x),x),x)^2+f1*diff(y(x),x)*diff(diff(y(x),x),x)+f2*y(x)*diff(diff(y(x),x),x)+g0*diff(y(x),x)^2+g1*y(x)*diff(y(x),x)+h*y(x)^2 = 0, y(x),'implicit')
Maple raw output
ln(y(x))-Int(RootOf(x-2*Intat(1/(-2*f0*_f^2-_f*f1+(-4*_f^2*f0*g0+_f^2*f1^2-4*_f*f0*g1+2*_f*f1*f2-4*f0*h+f2^2)^(1/2)-f2)*f0,_f = _Z)+_C1),x)-_C2 = 0, ln(y(x))-Int(RootOf(x+2*Intat(1/(2*f0*_f^2+_f*f1+(-4*_f^2*f0*g0+_f^2*f1^2-4*_f*f0*g1+2*_f*f1*f2-4*f0*h+f2^2)^(1/2)+f2)*f0,_f = _Z)+_C1),x)-_C2 = 0