ODE
\[ y''(x)+\left (e^{2 y(x)}+x\right ) y'(x)^3=0 \] ODE Classification
[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✗
cpu = 2.03804 (sec), leaf count = 0 , could not solve
DSolve[(E^(2*y[x]) + x)*Derivative[1][y][x]^3 + Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.165 (sec), leaf count = 26
\[ \left \{ {\frac {2\,{{\rm e}^{3\,y \left ( x \right ) }}}{3}}-2\,x{{\rm e}^{y \left ( x \right ) }}+{\it \_C1}-{\it \_C2}\,{{\rm e}^{2\,y \left ( x \right ) }}=0 \right \} \] Mathematica raw input
DSolve[(E^(2*y[x]) + x)*y'[x]^3 + y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[(E^(2*y[x]) + x)*Derivative[1][y][x]^3 + Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)+(x+exp(2*y(x)))*diff(y(x),x)^3 = 0, y(x),'implicit')
Maple raw output
2/3*exp(3*y(x))-2*x*exp(y(x))+_C1-_C2*exp(2*y(x)) = 0