Internal problem ID [9064]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1485.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (x -2\right ) x y^{\prime \prime \prime }-\left (x -2\right ) x y^{\prime \prime }-2 y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 47
dsolve((x-2)*x*diff(diff(diff(y(x),x),x),x)-(x-2)*x*diff(diff(y(x),x),x)-2*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2}+c_{2} {\mathrm e}^{x}+c_{3} \left (\frac {x^{2} \ln \left (x -2\right )}{4}-\frac {x^{2} \ln \relax (x )}{4}+\expIntegral \left (1, x -2\right ) {\mathrm e}^{x -2}+\frac {x}{2}+\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 50
DSolve[2*y[x] - 2*y'[x] - (-2 + x)*x*y''[x] + (-2 + x)*x*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} c_3 \left (-2 e^{x-2} \text {Ei}(2-x)+x^2 \tanh ^{-1}(1-x)+x+1\right )+c_1 x^2+c_2 e^x \\ \end{align*}