Internal problem ID [7983]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 507.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (4+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 108
dsolve((4+x)*diff(y(x),x$2)+(2+x)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} x \left (x^{3}+12 x^{2}+48 x +64\right )-\frac {c_{2} \left ({\mathrm e}^{-4} \operatorname {expIntegral}_{1}\left (-x -4\right ) x^{4}+12 \,{\mathrm e}^{-4} \operatorname {expIntegral}_{1}\left (-x -4\right ) x^{3}+{\mathrm e}^{x} x^{3}+48 \,{\mathrm e}^{-4} \operatorname {expIntegral}_{1}\left (-x -4\right ) x^{2}+9 \,{\mathrm e}^{x} x^{2}+64 \,{\mathrm e}^{-4} \operatorname {expIntegral}_{1}\left (-x -4\right ) x +22 x \,{\mathrm e}^{x}+6 \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x}}{24} \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 97
DSolve[(4+x)*y''[x]+(2+x)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^{-x-4} \left (c_2 x (x+4)^3 \operatorname {ExpIntegralEi}(x+4)+e^4 \left (24 c_1 x^4+x^3 \left (288 c_1-c_2 e^x\right )+9 x^2 \left (128 c_1-c_2 e^x\right )+2 x \left (768 c_1-11 c_2 e^x\right )-6 c_2 e^x\right )\right ) \]