ODE
\[ y''(x)+y(x) y'(x)=y(x)^3 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 122.766 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[1][y][x] + Derivative[2][y][x] == y[x]^3, y[x], x]
Maple ✓
cpu = 0.105 (sec), leaf count = 253
\[ \left \{ \int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}-{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( -{\frac {1}{2}\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}+{\frac {{{\it \_a}}^{2}}{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}}-{\frac {i}{2}}\sqrt {3} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}+{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( -{\frac {1}{2}\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}+{\frac {{{\it \_a}}^{2}}{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}}+{\frac {i}{2}}\sqrt {3} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}+{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y'[x] + y''[x] == y[x]^3,y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[1][y][x] + Derivative[2][y][x] == y[x]^3, y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x)*diff(y(x),x) = y(x)^3, y(x),'implicit')
Maple raw output
Intat(1/(1/2*_a^2+1/2*((_C1+(_a^6+_C1^2)^(1/2))^(1/3)-_a^2/(_C1+(_a^6+_C1^2)^(1/2))^(1/3))^2),_a = y(x))-x-_C2 = 0, Intat(1/(1/2*_a^2+1/2*(-1/2*(_C1+(_a^6+_C1^2)^(1/2))^(1/3)+1/2*_a^2/(_C1+(_a^6+_C1^2)^(1/2))^(1/3)-1/2*I*3^(1/2)*((_C1+(_a^6+_C1^2)^(1/2))^(1/3)+_a^2/(_C1+(_a^6+_C1^2)^(1/2))^(1/3)))^2),_a = y(x))-x-_C2 = 0, Intat(1/(1/2*_a^2+1/2*(-1/2*(_C1+(_a^6+_C1^2)^(1/2))^(1/3)+1/2*_a^2/(_C1+(_a^6+_C1^2)^(1/2))^(1/3)+1/2*I*3^(1/2)*((_C1+(_a^6+_C1^2)^(1/2))^(1/3)+_a^2/(_C1+(_a^6+_C1^2)^(1/2))^(1/3)))^2),_a = y(x))-x-_C2 = 0