59.1.787 problem 809

Internal problem ID [9959]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 809
Date solved : Monday, January 27, 2025 at 06:16:10 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} u^{\prime \prime }+2 u^{\prime }+u&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(u(x),x$2)+2*diff(u(x),x)+u(x)=0,u(x), singsol=all)
 

\[ u = {\mathrm e}^{-x} \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[D[u[x],{x,2}]+2*D[u[x],x]+u[x]==0,u[x],x,IncludeSingularSolutions -> True]
 

\[ u(x)\to e^{-x} (c_2 x+c_1) \]