64.10.35 problem 35

Internal problem ID [13362]
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 : 35
Date solved : Wednesday, March 05, 2025 at 09:49:02 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+13*y(x) = 0; 
ic:=y(0) = 3, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

ode=D[y[x],{x,2}]+6*D[y[x],x]+13*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} (4 \sin (2 x)+3 \cos (2 x)) \]

✓ Sympy. Time used: 0.182 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(13*y(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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