64.10.34 problem 34

Internal problem ID [13440]
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 : 34
Date solved : Tuesday, January 28, 2025 at 05:42:35 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+58 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 23

dsolve([diff(y(x),x$2)+6*diff(y(x),x)+58*y(x)=0,y(0) = -1, D(y)(0) = 5],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-3 x} \left (2 \sin \left (7 x \right )-7 \cos \left (7 x \right )\right )}{7} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 27

DSolve[{D[y[x],{x,2}]+6*D[y[x],x]+58*y[x]==0,{y[0]==-1,Derivative[1][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{7} e^{-3 x} (2 \sin (7 x)-7 \cos (7 x)) \]