Internal problem ID [8141]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 666.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+x*diff(y(x),x)+(2+x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \operatorname {KummerM}\left (\frac {3}{2}, \frac {1}{2}, -\frac {\left (x -2\right )^{2}}{2}\right )+c_{2} {\mathrm e}^{-x} \operatorname {KummerU}\left (\frac {3}{2}, \frac {1}{2}, -\frac {\left (x -2\right )^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.273 (sec). Leaf size: 94
DSolve[y''[x]+x*y'[x]+(2+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-\frac {x^2}{2}+x-\frac {9}{2}} \left (e^{5/2} \sqrt {2 \pi } c_2 \left (x^2-4 x+3\right ) \text {erfi}\left (\frac {x-2}{\sqrt {2}}\right )+4 e^{9/2} c_1 \left (x^2-4 x+3\right )-2 c_2 e^{\frac {1}{2} (x-3)^2+x} (x-2)\right ) \]