Internal problem ID [9065]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1486.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x -1\right ) y^{\prime \prime \prime }-8 y^{\prime } x +8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 50
dsolve((2*x-1)*diff(diff(diff(y(x),x),x),x)-8*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} \left (-\frac {x \,{\mathrm e}^{-1} \expIntegral \left (1, 2 x -1\right )}{2}+\frac {\expIntegral \left (1, 4 x -2\right ) {\mathrm e}^{2 x -2}}{4}+\frac {{\mathrm e}^{-2 x}}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 63
DSolve[8*y[x] - 8*x*y'[x] + (-1 + 2*x)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (\frac {c_3 \left (e^{2 x} \text {Ei}(2-4 x)-2 e x \text {Ei}(1-2 x)\right )}{e^2}+4 c_1 x-e^{-2 x} \left (4 c_2 e^{4 x}+c_3\right )\right ) \\ \end{align*}