68.2.4 problem 9

Internal problem ID [17132]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 9
Date solved : Thursday, October 02, 2025 at 01:44:12 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+45 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)+45*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} \left (c_1 \sin \left (6 x \right )+c_2 \cos \left (6 x \right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 26

ode=D[y[x],{x,2}]-6*D[y[x],x]+45*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{3 x} (c_2 \cos (6 x)+c_1 \sin (6 x)) \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(45*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (6 x \right )} + C_{2} \cos {\left (6 x \right )}\right ) e^{3 x} \]