Internal problem ID [7030]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 300.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+y^{\prime } x -2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(x*diff(y(x),x$2)+x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x^{2}+2 x \right )+c_{2} \left (\frac {\left (-x -1\right ) {\mathrm e}^{-x}}{2}+\frac {x \,\operatorname {Ei}_{1}\left (x \right ) \left (x +2\right )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 39
DSolve[x*y''[x]+x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x (x+2)-\frac {1}{2} c_2 e^{-x} \left (e^x (x+2) x \operatorname {ExpIntegralEi}(-x)+x+1\right ) \\ \end{align*}