ODE
\[ x^2 y'''(x)-x (1-y(x)) y''(x)+x y'(x)^2+(1-y(x)) y'(x)=0 \] ODE Classification
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.181587 (sec), leaf count = 282
\[\left \{\left \{y(x)\to \frac {2 \left (c_3 \left (J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-\frac {1}{4} i \sqrt {c_1} x \left (J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}-1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}+1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )\right )\right )+Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-\frac {1}{4} i \sqrt {c_1} x \left (Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}-1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}+1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )\right )\right )}{c_3 J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )+Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )}\right \}\right \}\]
Maple ✓
cpu = 1.217 (sec), leaf count = 190
\[ \left \{ \ln \left ( x \right ) +2\,\int ^{y \left ( x \right ) }\! \left ( 2\, \left ( {\it RootOf} \left ( -2\,\sqrt {4+{\it \_C1}}{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}+2\,{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}\,{\it \_h}-4\,{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}+2\,\sqrt {2}{{\sl Y}_{1/2\,\sqrt {4+{\it \_C1}}+1}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_C2}\,{\it \_Z}+2\,\sqrt {2}{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}+1}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_Z}-2\,{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}\sqrt {4+{\it \_C1}}+2\,{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )}{\it \_h}-4\,{{\sl J}_{1/2\,\sqrt {4+{\it \_C1}}}\left (1/2\,\sqrt {2}{\it \_Z}\right )} \right ) \right ) ^{2}+{{\it \_h}}^{2}-{\it \_C1}-4\,{\it \_h} \right ) ^{-1}{d{\it \_h}}-{\it \_C3}=0 \right \} \] Mathematica raw input
DSolve[(1 - y[x])*y'[x] + x*y'[x]^2 - x*(1 - y[x])*y''[x] + x^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*(BesselY[Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]] - (I/4)*x*(BesselY[-1 + Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]] - BesselY[1 + Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]])*Sqrt[C[1]] + (BesselJ[Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]] - (I/4)*x*(BesselJ[-1 + Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]] - BesselJ[1 + Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]])*Sqrt[C[1]])*C[3]))/(BesselY[Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]] + BesselJ[Sqrt[2 + C[2]]/Sqrt[2], (-I/2)*x*Sqrt[C[1]]]*C[3])}}
Maple raw input
dsolve(x^2*diff(diff(diff(y(x),x),x),x)-(1-y(x))*x*diff(diff(y(x),x),x)+x*diff(y(x),x)^2+(1-y(x))*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
ln(x)+2*Intat(1/(2*RootOf(-2*(4+_C1)^(1/2)*BesselY(1/2*(4+_C1)^(1/2),1/2*2^(1/2)*_Z)*_C2+2*BesselY(1/2*(4+_C1)^(1/2),1/2*2^(1/2)*_Z)*_C2*_h-4*BesselY(1/2*(4+_C1)^(1/2),1/2*2^(1/2)*_Z)*_C2+2*2^(1/2)*BesselY(1/2*(4+_C1)^(1/2)+1,1/2*2^(1/2)*_Z)*_C2*_Z+2*2^(1/2)*BesselJ(1/2*(4+_C1)^(1/2)+1,1/2*2^(1/2)*_Z)*_Z-2*BesselJ(1/2*(4+_C1)^(1/2),1/2*2^(1/2)*_Z)*(4+_C1)^(1/2)+2*BesselJ(1/2*(4+_C1)^(1/2),1/2*2^(1/2)*_Z)*_h-4*BesselJ(1/2*(4+_C1)^(1/2),1/2*2^(1/2)*_Z))^2+_h^2-_C1-4*_h),_h = y(x))-_C3 = 0