Internal problem ID [6805]
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]]
Solve \begin {gather*} \boxed {\left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-x} x \left (4+x \right )^{3}+c_{2} \left ({\mathrm e}^{-4-x} x \left (4+x \right )^{3} \expIntegral \left (1, -4-x \right )+x^{3}+9 x^{2}+22 x +6\right ) \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 54
DSolve[(4+x)*y''[x]+(2+x)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \left (e^{-x-4} x (x+4)^3 \left (c_2 \text {Ei}(x+4)+24 e^4 c_1\right )-c_2 (x (x (x+9)+22)+6)\right ) \\ \end{align*}