Internal problem ID [9066]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1487.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (2 x -1\right ) y^{\prime \prime \prime }+\left (4+x \right ) y^{\prime \prime }+2 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 38
dsolve((2*x-1)*diff(diff(diff(y(x),x),x),x)+(x+4)*diff(diff(y(x),x),x)+2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (c_{3}+\int \frac {\left (2 x c_{1}+c_{2}\right ) {\mathrm e}^{\frac {x}{2}}}{\left (2 x -1\right )^{\frac {3}{4}}}d x \right ) {\mathrm e}^{-\frac {x}{2}}}{\left (2 x -1\right )^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 0.418 (sec). Leaf size: 66
DSolve[2*y'[x] + (4 + x)*y''[x] + (-1 + 2*x)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 \\ \end{align*}