ODE
\[ y(x) y''(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3+\text {a4} y(x)^4+y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 103.101 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[2][y][x] == a0 + a1*y[x] + a2*y[x]^2 + a3*y[x]^3 + a4*y[x]^4 + Derivative[1][y][x]^2, y[x], x]
Maple ✓
cpu = 0.172 (sec), leaf count = 99
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {{\it a4}\,{{\it \_a}}^{4}+2\,{{\it \_a}}^{2}\ln \left ( {\it \_a} \right ) {\it a2}+2\,{{\it \_a}}^{3}{\it a3}+{{\it \_a}}^{2}{\it \_C1}-2\,{\it a1}\,{\it \_a}-{\it a0}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {{\it a4}\,{{\it \_a}}^{4}+2\,{{\it \_a}}^{2}\ln \left ( {\it \_a} \right ) {\it a2}+2\,{{\it \_a}}^{3}{\it a3}+{{\it \_a}}^{2}{\it \_C1}-2\,{\it a1}\,{\it \_a}-{\it a0}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y''[x] == a0 + a1*y[x] + a2*y[x]^2 + a3*y[x]^3 + a4*y[x]^4 + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[2][y][x] == a0 + a1*y[x] + a2*y[x]^2 + a3*y[x]^3 + a4*y[x]^4 + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3+a4*y(x)^4, y(x),'implicit')
Maple raw output
Intat(1/(a4*_a^4+2*_a^2*ln(_a)*a2+2*_a^3*a3+_a^2*_C1-2*a1*_a-a0)^(1/2),_a = y(x))-x-_C2 = 0, Intat(-1/(a4*_a^4+2*_a^2*ln(_a)*a2+2*_a^3*a3+_a^2*_C1-2*a1*_a-a0)^(1/2),_a = y(x))-x-_C2 = 0