Internal problem ID [7958]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 481.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +2\right ) y^{\prime \prime }+x y^{\prime }+3 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 115
dsolve((2+x)*diff(y(x),x$2)+x*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \left (x^{5}-20 x^{3}-40 x^{2}+32\right )-\frac {c_{2} \left (\operatorname {expIntegral}_{1}\left (-2-x \right ) {\mathrm e}^{-2} x^{5}+{\mathrm e}^{x} x^{4}-20 \,{\mathrm e}^{-2} \operatorname {expIntegral}_{1}\left (-2-x \right ) x^{3}-{\mathrm e}^{x} x^{3}-40 \,{\mathrm e}^{-2} \operatorname {expIntegral}_{1}\left (-2-x \right ) x^{2}-18 \,{\mathrm e}^{x} x^{2}-22 x \,{\mathrm e}^{x}+32 \,{\mathrm e}^{-2} \operatorname {expIntegral}_{1}\left (-2-x \right )+8 \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x}}{240} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 81
DSolve[(2+x)*y''[x]+x*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{960} e^{-x-1} \left (c_2 \left (x^2-6 x+4\right ) (x+2)^3 \operatorname {ExpIntegralEi}(x+2)+3840 c_1 \left (x^2-6 x+4\right ) (x+2)^3-c_2 e^{x+2} \left (x^4-x^3-18 x^2-22 x+8\right )\right ) \]