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 = 0.198287 (sec), leaf count = 83
\[\left \{\left \{y(x)\to -\frac {a c_1+\sqrt {c_1^3 \left (c_3+x\right ){}^2-e^{2 c_2} c_1}}{c_1}\right \},\left \{y(x)\to \frac {\sqrt {c_1^3 \left (c_3+x\right ){}^2-e^{2 c_2} c_1}-a c_1}{c_1}\right \}\right \}\]
Maple ✓
cpu = 0.296 (sec), leaf count = 95
\[ \left \{ \ln \left ( a+y \left ( x \right ) \right ) -\int \!{\it RootOf} \left ( -2\,\int ^{{\it \_Z}}\!{\frac {{\it \_C1}}{-4\,{\it \_C1}\,{{\it \_h}}^{2}+1+\sqrt {-4\,{\it \_C1}\,{{\it \_h}}^{2}+1}}}{d{\it \_h}}+x+{\it \_C2} \right ) \,{\rm d}x-{\it \_C3}=0,\ln \left ( a+y \left ( x \right ) \right ) -\int \!{\it RootOf} \left ( 2\,\int ^{{\it \_Z}}\!{\frac {{\it \_C1}}{4\,{\it \_C1}\,{{\it \_h}}^{2}+\sqrt {-4\,{\it \_C1}\,{{\it \_h}}^{2}+1}-1}}{d{\it \_h}}+x+{\it \_C2} \right ) \,{\rm d}x-{\it \_C3}=0 \right \} \] 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),'implicit')
Maple raw output
ln(a+y(x))-Int(RootOf(-2*Intat(_C1/(-4*_C1*_h^2+1+(-4*_C1*_h^2+1)^(1/2)),_h = _Z)+x+_C2),x)-_C3 = 0, ln(a+y(x))-Int(RootOf(2*Intat(1/(4*_C1*_h^2+(-4*_C1*_h^2+1)^(1/2)-1)*_C1,_h = _Z)+x+_C2),x)-_C3 = 0