38.1.13 problem 15

Internal problem ID [8174]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 05:18:07 PM
CAS classification : [[_2nd_order, _missing_x]]

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

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

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+13*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} \left (c_1 \sin \left (2 x \right )+c_2 \cos \left (2 x \right )\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to e^{3 x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \end{align*}

✓ Sympy. Time used: 0.094 (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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

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