64.10.10 problem 10

Internal problem ID [13416]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:42:05 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-3 x} \left (c_{1} \sin \left (4 x \right )+c_{2} \cos \left (4 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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