81.4.1 problem 1

Internal problem ID [18655]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 48
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 12:08:53 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.565 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_2 e^x+c_1\right ) \]