ODE
\[ (1-2 x) y'''(x)-(x+4) y''(x)-2 y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.91447 (sec), leaf count = 66
\[\left \{\left \{y(x)\to \int _1^xe^{-\frac {K[1]}{2}} \left (\frac {2 \sqrt {2} c_1 K[1]}{(2 K[1]-1)^{5/4}}+c_2 L_{-\frac {1}{4}}^{\frac {5}{4}}\left (\frac {K[1]}{2}-\frac {1}{4}\right )\right )dK[1]+c_3\right \}\right \}\]
Maple ✓
cpu = 0.835 (sec), leaf count = 45
\[\left [y \left (x \right ) = \frac {\left (\textit {\_C3} +\int \frac {\left (2 \textit {\_C1} x +\textit {\_C2} \right ) \left (-1+2 x \right )^{\frac {1}{4}} {\mathrm e}^{\frac {x}{2}}}{1-2 x}d x \right ) {\mathrm e}^{-\frac {x}{2}}}{\left (-1+2 x \right )^{\frac {1}{4}}}\right ]\] Mathematica raw input
DSolve[-2*y'[x] - (4 + x)*y''[x] + (1 - 2*x)*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3] + Inactive[Integrate][((2*Sqrt[2]*C[1]*K[1])/(-1 + 2*K[1])^(5/4) + C[2]*LaguerreL[-1/4, 5/4, -1/4 + K[1]/2])/E^(K[1]/2), {K[1], 1, x}]}}
Maple raw input
dsolve((1-2*x)*diff(diff(diff(y(x),x),x),x)-(4+x)*diff(diff(y(x),x),x)-2*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = (_C3+Int((2*_C1*x+_C2)*(-1+2*x)^(1/4)*exp(1/2*x)/(1-2*x),x))*exp(-1/2*x)/(-1+2*x)^(1/4)]