Internal problem ID [7326]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 606.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 36
dsolve(x^2*diff(y(x),x$2)+x*(2+x)*diff(y(x),x)-(2-3*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \,{\mathrm e}^{-x}+\frac {c_{2} \left (x^{3} {\mathrm e}^{-x} \expIntegral \left (1, -x \right )+x^{2}+x +2\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 41
DSolve[x^2*y''[x]+x*(2+x)*y'[x]-(2-3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-x} x (c_2 \operatorname {Ei}(x)+6 c_1)-\frac {c_2 \left (x^2+x+2\right )}{6 x^2} \\ \end{align*}