76.13.2 problem 2

Internal problem ID [17584]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 10:44:32 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 20

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

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