2.1486   ODE No. 1486

\[ (2 x-1) y^{(3)}(x)-8 x y'(x)+8 y(x)=0 \]

✓ Mathematica : cpu = 0.710633 (sec), leaf count = 65

DSolve[8*y[x] - 8*x*Derivative[1][y][x] + (-1 + 2*x)*Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{4} c_3 x \left (\frac {e^{2 x-2} \text {Ei}(2-4 x)}{x}-\frac {2 \text {Ei}(1-2 x)}{e}-\frac {e^{-2 x}}{x}\right )+c_1 x-c_2 e^{2 x}\right \}\right \}\]

✓ Maple : cpu = 0.249 (sec), leaf count = 51

dsolve((2*x-1)*diff(diff(diff(y(x),x),x),x)-8*x*diff(y(x),x)+8*y(x)=0,y(x))
 

\[y \left (x \right ) = x c_{1} +c_{2} {\mathrm e}^{2 x}-\frac {c_{3} \left (2 x \,{\mathrm e}^{-1} \operatorname {Ei}_{1}\left (2 x -1\right )-\operatorname {Ei}_{1}\left (-2+4 x \right ) {\mathrm e}^{2 x -2}-{\mathrm e}^{-2 x}\right )}{4}\]