ODE
\[ (a+y(x)) y'''(x)+3 y'(x) y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.375826 (sec), leaf count = 83
\[\left \{\left \{y(x)\to -\frac {a c_1+\sqrt {c_1{}^3 (x+c_3){}^2-e^{2 c_2} c_1}}{c_1}\right \},\left \{y(x)\to \frac {\sqrt {c_1{}^3 (x+c_3){}^2-e^{2 c_2} c_1}-a c_1}{c_1}\right \}\right \}\]
Maple ✓
cpu = 4.607 (sec), leaf count = 115
\[\left [y \left (x \right ) = {\mathrm e}^{\int \RootOf \left (2 x \,\textit {\_C1}^{\frac {3}{2}} \textit {\_Z} +2 \textit {\_C2} \,\textit {\_C1}^{\frac {3}{2}} \textit {\_Z} -\left (-4 \textit {\_Z}^{2}+\textit {\_C1} \right )^{\frac {3}{2}}-4 \sqrt {-4 \textit {\_Z}^{2}+\textit {\_C1}}\, \textit {\_Z}^{2}-\textit {\_C1}^{\frac {3}{2}}\right )d x +\textit {\_C3}}-a, y \left (x \right ) = {\mathrm e}^{\int \RootOf \left (2 x \,\textit {\_C1}^{\frac {3}{2}} \textit {\_Z} +2 \textit {\_C2} \,\textit {\_C1}^{\frac {3}{2}} \textit {\_Z} +\left (-4 \textit {\_Z}^{2}+\textit {\_C1} \right )^{\frac {3}{2}}+4 \sqrt {-4 \textit {\_Z}^{2}+\textit {\_C1}}\, \textit {\_Z}^{2}-\textit {\_C1}^{\frac {3}{2}}\right )d x +\textit {\_C3}}-a\right ]\] Mathematica raw input
DSolve[3*y'[x]*y''[x] + (a + y[x])*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((a*C[1] + Sqrt[-(E^(2*C[2])*C[1]) + C[1]^3*(x + C[3])^2])/C[1])}, {y[x] -> (-(a*C[1]) + Sqrt[-(E^(2*C[2])*C[1]) + C[1]^3*(x + C[3])^2])/C[1]}}
Maple raw input
dsolve((a+y(x))*diff(diff(diff(y(x),x),x),x)+3*diff(y(x),x)*diff(diff(y(x),x),x) = 0, y(x))
Maple raw output
[y(x) = exp(Int(RootOf(2*x*_C1^(3/2)*_Z+2*_C2*_C1^(3/2)*_Z-(-4*_Z^2+_C1)^(3/2)-4*(-4*_Z^2+_C1)^(1/2)*_Z^2-_C1^(3/2)),x)+_C3)-a, y(x) = exp(Int(RootOf(2*x*_C1^(3/2)*_Z+2*_C2*_C1^(3/2)*_Z+(-4*_Z^2+_C1)^(3/2)+4*(-4*_Z^2+_C1)^(1/2)*_Z^2-_C1^(3/2)),x)+_C3)-a]