50.1.32 problem 5

Internal problem ID [7804]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 5
Date solved : Wednesday, March 05, 2025 at 05:06:23 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \end{align*}

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

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=D[y[x],{x,2}]-5*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (c_2 e^{3 x}+c_1\right ) \]

✓ Sympy. Time used: 0.141 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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