Internal problem ID [6809]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 77.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (3+x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve((3+x)*diff(y(x),x$2)+(1+2*x)*diff(y(x),x)-(2-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-x} x \left (6+x \right ) \left (x^{2}+9 x +27\right ) \left (x^{2}+3 x +9\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 29
DSolve[(3+x)*y''[x]+(1+2*x)*y'[x]-(2-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-x-3} \left (c_2 (x+3)^6+6 c_1\right ) \\ \end{align*}