2.1842 ODE No. 1842
\[ x^2 y^{(3)}(x)+x (y(x)-1) y''(x)+x y'(x)^2+(1-y(x)) y'(x)=0 \]
✓ Mathematica : cpu = 0.213379 (sec), leaf count = 286
DSolve[(1 - y[x])*Derivative[1][y][x] + x*Derivative[1][y][x]^2 + x*(-1 + y[x])*Derivative[2][y][x] + x^2*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {2 x \left (c_3 \left (J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-\frac {1}{4} i \sqrt {c_1} x \left (J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}-1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}+1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )\right )\right )+Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-\frac {1}{4} i \sqrt {c_1} x \left (Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}-1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )-Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}+1}\left (-\frac {1}{2} i x \sqrt {c_1}\right )\right )\right )}{c_3 x J_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )+x Y_{\frac {\sqrt {c_2+2}}{\sqrt {2}}}\left (-\frac {1}{2} i x \sqrt {c_1}\right )}\right \}\right \}\]
✓ Maple : cpu = 0.659 (sec), leaf count = 190
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+x*(-1+y(x))*diff(diff(y(x),x),x)+x*diff(y(x),x)^2+(1-y(x))*diff(y(x),x)=0,y(x))
\[\ln \left (x \right )+2 \left (\int _{}^{y \left (x \right )}\frac {1}{2 \operatorname {RootOf}\left (-2 \sqrt {4+c_{1}}\, \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) c_{2} +2 \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) c_{2} \textit {\_h} -4 \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) c_{2} +2 \sqrt {2}\, \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}+1, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) c_{2} \textit {\_Z} +2 \sqrt {2}\, \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}+1, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) \textit {\_Z} -2 \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) \sqrt {4+c_{1}}+2 \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) \textit {\_h} -4 \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right )\right )^{2}+\textit {\_h}^{2}-c_{1} -4 \textit {\_h}}d \textit {\_h} \right )-c_{3} = 0\]