59.1.787 problem 809

Internal problem ID [9959]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 809
Date solved : Wednesday, March 05, 2025 at 08:01:27 AM
CAS classification : [[_2nd_order, _missing_x]]

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

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

ode:=diff(diff(u(x),x),x)+2*diff(u(x),x)+u(x) = 0; 
dsolve(ode,u(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.147 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
u = Function("u") 
ode = Eq(u(x) + 2*Derivative(u(x), x) + Derivative(u(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=u(x),ics=ics)
 

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