56.1.40 problem 41

Internal problem ID [8752]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 41
Date solved : Monday, January 27, 2025 at 04:46:41 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

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

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

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