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 = 3.75424 (sec), leaf count = 0 , could not solve
DSolve[h*y[x]^2 + g1*y[x]*Derivative[1][y][x] + g0*Derivative[1][y][x]^2 + f2*y[x]*Derivative[2][y][x] + f1*Derivative[1][y][x]*Derivative[2][y][x] + f0*Derivative[2][y][x]^2 == 0, y[x], x]
Maple ✓
cpu = 4.672 (sec), leaf count = 142
\[\left [y \left (x \right ) = 0, y \left (x \right ) = {\mathrm e}^{\int \RootOf \left (x -2 \left (\int _{}^{\textit {\_Z}}\frac {\mathit {f0}}{-2 \textit {\_f}^{2} \mathit {f0} -\textit {\_f} \mathit {f1} +\sqrt {-4 \textit {\_f}^{2} \mathit {f0} \mathit {g0} +\textit {\_f}^{2} \mathit {f1}^{2}-4 \textit {\_f} \mathit {f0} \mathit {g1} +2 \textit {\_f} \mathit {f1} \mathit {f2} -4 \mathit {f0} h +\mathit {f2}^{2}}-\mathit {f2}}d \textit {\_f} \right )+\textit {\_C1} \right )d x +\textit {\_C2}}, y \left (x \right ) = {\mathrm e}^{\int \RootOf \left (x +2 \left (\int _{}^{\textit {\_Z}}\frac {\mathit {f0}}{2 \textit {\_f}^{2} \mathit {f0} +\textit {\_f} \mathit {f1} +\sqrt {-4 \textit {\_f}^{2} \mathit {f0} \mathit {g0} +\textit {\_f}^{2} \mathit {f1}^{2}-4 \textit {\_f} \mathit {f0} \mathit {g1} +2 \textit {\_f} \mathit {f1} \mathit {f2} -4 \mathit {f0} h +\mathit {f2}^{2}}+\mathit {f2}}d \textit {\_f} \right )+\textit {\_C1} \right )d x +\textit {\_C2}}\right ]\] 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
DSolve[h*y[x]^2 + g1*y[x]*Derivative[1][y][x] + g0*Derivative[1][y][x]^2 + f2*y[x]*Derivative[2][y][x] + f1*Derivative[1][y][x]*Derivative[2][y][x] + f0*Derivative[2][y][x]^2 == 0, y[x], x]
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))
Maple raw output
[y(x) = 0, y(x) = exp(Int(RootOf(x-2*Intat(1/(-2*_f^2*f0-_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), y(x) = exp(Int(RootOf(x+2*Intat(1/(2*_f^2*f0+_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)]