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 = 0.353271 (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 = 3.327 (sec), leaf count = 190
\[\left [\ln \left (x \right )+2 \left (\int _{}^{y \left (x \right )}\frac {1}{2 \RootOf \left (-2 \BesselY \left (\frac {\sqrt {4+\textit {\_C1}}}{2}, \frac {\textit {\_Z} \sqrt {2}}{2}\right ) \sqrt {4+\textit {\_C1}}\, \textit {\_C2} +2 \BesselY \left (\frac {\sqrt {4+\textit {\_C1}}}{2}, \frac {\textit {\_Z} \sqrt {2}}{2}\right ) \textit {\_C2} \textit {\_h} +2 \BesselY \left (\frac {\sqrt {4+\textit {\_C1}}}{2}+1, \frac {\textit {\_Z} \sqrt {2}}{2}\right ) \sqrt {2}\, \textit {\_C2} \textit {\_Z} -4 \BesselY \left (\frac {\sqrt {4+\textit {\_C1}}}{2}, \frac {\textit {\_Z} \sqrt {2}}{2}\right ) \textit {\_C2} +2 \BesselJ \left (\frac {\sqrt {4+\textit {\_C1}}}{2}+1, \frac {\textit {\_Z} \sqrt {2}}{2}\right ) \sqrt {2}\, \textit {\_Z} -2 \BesselJ \left (\frac {\sqrt {4+\textit {\_C1}}}{2}, \frac {\textit {\_Z} \sqrt {2}}{2}\right ) \sqrt {4+\textit {\_C1}}+2 \BesselJ \left (\frac {\sqrt {4+\textit {\_C1}}}{2}, \frac {\textit {\_Z} \sqrt {2}}{2}\right ) \textit {\_h} -4 \BesselJ \left (\frac {\sqrt {4+\textit {\_C1}}}{2}, \frac {\textit {\_Z} \sqrt {2}}{2}\right )\right )^{2}+\textit {\_h}^{2}-\textit {\_C1} -4 \textit {\_h}}d \textit {\_h} \right )-\textit {\_C3} = 0\right ]\] 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], (-1/2*I)*x*Sqrt[C[1]]] - (I/4)*x*(BesselY[-1 + Sqrt[2 + C[2]]/Sqrt[2], (-1/2*I)*x*Sqrt[C[1]]] - BesselY[1 + Sqrt[2 + C[2]]/Sqrt[2], (-1/2*I)*x*Sqrt[C[1]]])*Sqrt[C[1]] + (BesselJ[Sqrt[2 + C[2]]/Sqrt[2], (-1/2*I)*x*Sqrt[C[1]]] - (I/4)*x*(BesselJ[-1 + Sqrt[2 + C[2]]/Sqrt[2], (-1/2*I)*x*Sqrt[C[1]]] - BesselJ[1 + Sqrt[2 + C[2]]/Sqrt[2], (-1/2*I)*x*Sqrt[C[1]]])*Sqrt[C[1]])*C[3]))/(BesselY[Sqrt[2 + C[2]]/Sqrt[2], (-1/2*I)*x*Sqrt[C[1]]] + BesselJ[Sqrt[2 + C[2]]/Sqrt[2], (-1/2*I)*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))
Maple raw output
[ln(x)+2*Intat(1/(2*RootOf(-2*BesselY(1/2*(4+_C1)^(1/2),1/2*_Z*2^(1/2))*(4+_C1)^(1/2)*_C2+2*BesselY(1/2*(4+_C1)^(1/2),1/2*_Z*2^(1/2))*_C2*_h+2*BesselY(1/2*(4+_C1)^(1/2)+1,1/2*_Z*2^(1/2))*2^(1/2)*_C2*_Z-4*BesselY(1/2*(4+_C1)^(1/2),1/2*_Z*2^(1/2))*_C2+2*BesselJ(1/2*(4+_C1)^(1/2)+1,1/2*_Z*2^(1/2))*2^(1/2)*_Z-2*BesselJ(1/2*(4+_C1)^(1/2),1/2*_Z*2^(1/2))*(4+_C1)^(1/2)+2*BesselJ(1/2*(4+_C1)^(1/2),1/2*_Z*2^(1/2))*_h-4*BesselJ(1/2*(4+_C1)^(1/2),1/2*_Z*2^(1/2)))^2+_h^2-_C1-4*_h),_h = y(x))-_C3 = 0]