78.2.1 problem 1.a

Internal problem ID [20953]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 1.a
Date solved : Thursday, October 02, 2025 at 07:00:38 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-9*diff(y(x),x)+20*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{x}+c_2 \right ) {\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

ode=D[y[x],{x,2}]-9*D[y[x],x]+20*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{4 x} \left (c_2 e^x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(20*y(x) - 9*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{x}\right ) e^{4 x} \]