Internal problem ID [9813]
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]]
\[ \boxed {\left (2 x -1\right ) y^{\prime \prime \prime }-8 y^{\prime } x +8 y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = c_{1} x +c_{2} {\mathrm e}^{2 x}-\frac {c_{3} x \,{\mathrm e}^{-1} \operatorname {expIntegral}_{1}\left (-1+2 x \right )}{2}+\frac {c_{3} \operatorname {expIntegral}_{1}\left (-2+4 x \right ) {\mathrm e}^{2 x -2}}{4}+\frac {c_{3} {\mathrm e}^{-2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.372 (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]
\[ y(x)\to \frac {1}{4} \left (c_3 e^{2 x-2} \operatorname {ExpIntegralEi}(2-4 x)-\frac {2 c_3 x \operatorname {ExpIntegralEi}(1-2 x)}{e}+4 c_1 x-4 c_2 e^{2 x}-c_3 e^{-2 x}\right ) \]