7.10.9 problem 9

Internal problem ID [279]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 9
Date solved : Wednesday, February 05, 2025 at 03:06:40 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+8*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-4 x} \left (c_1 \sin \left (3 x \right )+c_2 \cos \left (3 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]+8*D[y[x],x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} (c_2 \cos (3 x)+c_1 \sin (3 x)) \]