Internal problem ID [7565]
Book: Collection of Kovacic problems
Section: section 2. Solution found using all possible Kovacic cases
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 16
dsolve(x*diff(diff(y(x),x),x)-(2*x+2)*diff(y(x),x)+(2+x)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x^{3} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 23
DSolve[x*y''[x]-(2*x+2)*y'[x]+(2+x)*y[x] ==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^x \left (c_2 x^3+3 c_1\right ) \\ \end{align*}