Internal problem ID [8302]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 830.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(x*diff(y(x), x$2) +(1+x)*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \left (x -1\right )+c_{2} \left ({\mathrm e}^{-x} \left (x -1\right ) \operatorname {Ei}_{1}\left (-x \right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 33
DSolve[x*y''[x] +(1+x)*y'[x]+2*y[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_2 (x-1) \operatorname {ExpIntegralEi}(x)+c_1 (x-1)-c_2 e^x\right ) \]