89.11.21 problem 21

Internal problem ID [24546]
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 : 21
Date solved : Thursday, October 02, 2025 at 10:46:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 a y^{\prime }+3 a^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-4*a*diff(y(x),x)+3*a^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{a x} \left (c_1 +c_2 \,{\mathrm e}^{2 a x}\right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

ode=D[y[x],{x,2}] -4*a*D[y[x],x] +3*a^2*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{a x} \left (c_1 e^{2 a x}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(3*a**2*y(x) - 4*a*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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