64.10.34 problem 34

Internal problem ID [13369]
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 : Monday, March 31, 2025 at 07:52:32 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*}

✓ Maple. Time used: 0.070 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+58*y(x) = 0; 
ic:=y(0) = -1, D(y)(0) = 5; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.179 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(58*y(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

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