71.1.4 problem 18

Internal problem ID [14242]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 18
Date solved : Monday, March 31, 2025 at 12:13:56 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.149 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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