Internal problem ID [7982]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 506.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 89
dsolve((2+x)*diff(y(x),x$2)+(1+x)*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} x \left (x^{3}-12 x -16\right )-\frac {c_{2} \left ({\mathrm e}^{-2} \operatorname {expIntegral}_{1}\left (-2-x \right ) x^{4}+{\mathrm e}^{x} x^{3}-12 \,{\mathrm e}^{-2} \operatorname {expIntegral}_{1}\left (-2-x \right ) x^{2}-{\mathrm e}^{x} x^{2}-16 \,{\mathrm e}^{-2} \operatorname {expIntegral}_{1}\left (-2-x \right ) x -10 x \,{\mathrm e}^{x}-6 \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x}}{48} \]
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 99
DSolve[(2+x)*y''[x]+(1+x)*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x-1} \left (c_2 (x-4) (x+2)^2 x \operatorname {ExpIntegralEi}(x+2)+384 c_1 x^4-c_2 e^{x+2} x^3+x^2 \left (c_2 e^{x+2}-4608 c_1\right )+x \left (10 c_2 e^{x+2}-6144 c_1\right )+6 c_2 e^{x+2}\right )}{96 \sqrt {2}} \]