ODE
\[ y'(x)^3+y'(x)=e^{y(x)} \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 296.432 (sec), leaf count = 433
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt [3]{\sqrt {3} \sqrt {4+27 e^{2 K[1]}}-9 e^{K[1]}}}{\sqrt [3]{2} \left (\sqrt {3} \sqrt {4+27 e^{2 K[1]}}-9 e^{K[1]}\right )^{2/3}-2 \sqrt [3]{3}}dK[1]\& \right ]\left [-\frac {x}{6^{2/3}}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt [3]{\sqrt {3} \sqrt {4+27 e^{2 K[2]}}-9 e^{K[2]}}}{-i \sqrt [3]{2} 3^{2/3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[2]}}-9 e^{K[2]}\right )^{2/3}+\sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[2]}}-9 e^{K[2]}\right )^{2/3}-2 \sqrt {3}-6 i}dK[2]\& \right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt [3]{\sqrt {3} \sqrt {4+27 e^{2 K[3]}}-9 e^{K[3]}}}{i \sqrt [3]{2} 3^{2/3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[3]}}-9 e^{K[3]}\right )^{2/3}+\sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[3]}}-9 e^{K[3]}\right )^{2/3}-2 \sqrt {3}+6 i}dK[3]\& \right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.304 (sec), leaf count = 265
\[\left [x -\left (\int _{}^{y \left (x \right )}\frac {6 \left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}}{\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {2}{3}}-12}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}\frac {12 \left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}}{\left (1+i \sqrt {3}\right ) \left (\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}-\sqrt {3}+3 i\right ) \left (-\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}+3 i-\sqrt {3}\right )}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}-\frac {12 \left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}}{\left (-1+i \sqrt {3}\right ) \left (-\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}+\sqrt {3}+3 i\right ) \left (\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}+3 i+\sqrt {3}\right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x] + y'[x]^3 == E^y[x],y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][(-9*E^K[1] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[1])])^(1/3)/(-2*3^(1/3) + 2^(1/3)*(-9*E^K[1] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[1])])^(2/3)), {K[1], 1, #1}] & ][-(x/6^(2/3)) + C[1]]}, {y[x] -> InverseFunction[Inactive[Integrate][(-9*E^K[2] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[2])])^(1/3)/(-6*I - 2*Sqrt[3] + 2^(1/3)*3^(1/6)*(-9*E^K[2] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[2])])^(2/3) - I*2^(1/3)*3^(2/3)*(-9*E^K[2] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[2])])^(2/3)), {K[2], 1, #1}] & ][x/(2*2^(2/3)*3^(5/6)) + C[1]]}, {y[x] -> InverseFunction[Inactive[Integrate][(-9*E^K[3] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[3])])^(1/3)/(6*I - 2*Sqrt[3] + 2^(1/3)*3^(1/6)*(-9*E^K[3] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[3])])^(2/3) + I*2^(1/3)*3^(2/3)*(-9*E^K[3] + Sqrt[3]*Sqrt[4 + 27*E^(2*K[3])])^(2/3)), {K[3], 1, #1}] & ][x/(2*2^(2/3)*3^(5/6)) + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)^3+diff(y(x),x) = exp(y(x)), y(x))
Maple raw output
[x-Intat(6/((108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(2/3)-12)*(108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(1+I*3^(1/2))/((108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(1/3)-3^(1/2)+3*I)/(-(108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(1/3)+3*I-3^(1/2))*(108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(-12/(-1+I*3^(1/2))/(-(108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(1/3)+3^(1/2)+3*I)/((108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(1/3)+3*I+3^(1/2))*(108*exp(_a)+12*(12+81*exp(_a)^2)^(1/2))^(1/3),_a = y(x))-_C1 = 0]