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]]
\[ \boxed {y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 64
dsolve(diff(y(x),x$2)+x*diff(y(x),x)+(2+x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {1}{2} x^{2}+x} \left (x^{2}-4 x +3\right )+c_{2} {\mathrm e}^{-\frac {1}{2} x^{2}+x} \left (x^{2}-4 x +3\right ) \left (\int \frac {{\mathrm e}^{\frac {1}{2} x^{2}-2 x}}{\left (x -1\right )^{2} \left (x -3\right )^{2}}d x \right ) \]
✓ 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]
\[ y(x)\to \frac {1}{4} e^{-\frac {x^2}{2}+x-\frac {9}{2}} \left (e^{5/2} \sqrt {2 \pi } c_2 \left (x^2-4 x+3\right ) \text {erfi}\left (\frac {x-2}{\sqrt {2}}\right )+4 e^{9/2} c_1 \left (x^2-4 x+3\right )-2 c_2 e^{\frac {1}{2} (x-3)^2+x} (x-2)\right ) \]