ODE No. 1486

\[ (2 x-1) y^{(3)}(x)-8 x y'(x)+8 y(x)=0 \] Mathematica : cpu = 0.283482 (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 = 0.188 (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))
 

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