Internal problem ID [7526]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 809.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {u^{\prime \prime }+2 u^{\prime }+u=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 18
dsolve(diff(u(x),x$2)+2*diff(u(x),x)+u(x)=0,u(x), singsol=all)
\[ u \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[u''[x]+2*u'[x]+u[x]==0,u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to e^{-x} (c_2 x+c_1) \\ \end{align*}