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 = 0.267445 (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 = 0.506 (sec), leaf count = 572
\[\left [y \left (x \right ) = \ln \left (\frac {\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}{2}-\frac {2 \left (-x -\frac {\textit {\_C2}^{2}}{4}\right )}{\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}+\frac {\textit {\_C2}}{2}\right ), y \left (x \right ) = \ln \left (-\frac {\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}{4}+\frac {-x -\frac {\textit {\_C2}^{2}}{4}}{\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}+\frac {\textit {\_C2}}{2}-\frac {i \sqrt {3}\, \left (\frac {\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}{2}+\frac {-2 x -\frac {\textit {\_C2}^{2}}{2}}{\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}\right )}{2}\right ), y \left (x \right ) = \ln \left (-\frac {\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}{4}+\frac {-x -\frac {\textit {\_C2}^{2}}{4}}{\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}+\frac {\textit {\_C2}}{2}+\frac {i \sqrt {3}\, \left (\frac {\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}{2}+\frac {-2 x -\frac {\textit {\_C2}^{2}}{2}}{\left (6 \textit {\_C2} x -6 \textit {\_C1} +\textit {\_C2}^{3}+2 \sqrt {-3 \textit {\_C1} \,\textit {\_C2}^{3}-3 \textit {\_C2}^{2} x^{2}-18 \textit {\_C2} x \textit {\_C1} -16 x^{3}+9 \textit {\_C1}^{2}}\right )^{\frac {1}{3}}}\right )}{2}\right )\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))
Maple raw output
[y(x) = ln(1/2*(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)-2*(-x-1/4*_C2^2)/(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)+1/2*_C2), y(x) = ln(-1/4*(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)+(-x-1/4*_C2^2)/(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)+1/2*_C2-1/2*I*3^(1/2)*(1/2*(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)+2*(-x-1/4*_C2^2)/(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3))), y(x) = ln(-1/4*(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)+(-x-1/4*_C2^2)/(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)+1/2*_C2+1/2*I*3^(1/2)*(1/2*(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)+2*(-x-1/4*_C2^2)/(6*_C2*x-6*_C1+_C2^3+2*(-3*_C1*_C2^3-3*_C2^2*x^2-18*_C1*_C2*x-16*x^3+9*_C1^2)^(1/2))^(1/3)))]