Internal problem ID [7561]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 73.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (4+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 52
dsolve((4+x)*diff(y(x),x$2)+(2+x)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} x \left (x +4\right )^{3}+c_{2} \left ({\mathrm e}^{-x -4} x \left (x +4\right )^{3} \operatorname {Ei}_{1}\left (-x -4\right )+x^{3}+9 x^{2}+22 x +6\right ) \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 97
DSolve[(4+x)*y''[x]+(2+x)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^{-x-4} \left (c_2 x (x+4)^3 \operatorname {ExpIntegralEi}(x+4)+e^4 \left (24 c_1 x^4+x^3 \left (288 c_1-c_2 e^x\right )+9 x^2 \left (128 c_1-c_2 e^x\right )+2 x \left (768 c_1-11 c_2 e^x\right )-6 c_2 e^x\right )\right ) \]