89.11.22 problem 22

Internal problem ID [24547]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 22
Date solved : Thursday, October 02, 2025 at 10:46:01 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = c_1 \,{\mathrm e}^{a x}+c_2 \,{\mathrm e}^{b x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to c_2 e^{a x}+c_1 e^{b x} \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 15

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

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