Internal problem ID [6794]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 62.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.105 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+(x-3)*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \KummerM \left (\frac {3}{2}, \frac {1}{2}, -\frac {\left (x -3\right )^{2}}{2}\right )+c_{2} \KummerU \left (\frac {3}{2}, \frac {1}{2}, -\frac {\left (x -3\right )^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 58
DSolve[y''[x]+(x-3)*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 (x-4) (x-2) F\left (\frac {x-3}{\sqrt {2}}\right )}{\sqrt {2}}+c_1 e^{-\frac {1}{2} (x-6) x} (x-4) (x-2)-\frac {1}{2} c_2 (x-3) \\ \end{align*}