67.11.34 problem 17.6 (d)

Internal problem ID [16635]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.6 (d)
Date solved : Thursday, October 02, 2025 at 01:37:16 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.075 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+13*y(x) = 0; 
ic:=[y(0) = 1, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-4*D[y[x],x]+13*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} e^{2 x} (3 \cos (3 x)-2 \sin (3 x)) \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(13*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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