89.13.7 problem 7

Internal problem ID [24590]
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 127
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:46:20 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+7 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+7*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (c_1 \sin \left (\sqrt {3}\, x \right )+c_2 \cos \left (\sqrt {3}\, x \right )\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 34

ode=D[y[x],{x,2}]-4*D[y[x],{x,1}]+7*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x} \left (c_2 \cos \left (\sqrt {3} x\right )+c_1 \sin \left (\sqrt {3} x\right )\right ) \end{align*}

✓ Sympy. Time used: 0.033 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(7*y(x) - 3*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {\sqrt {21} x}{3}} + C_{2} e^{\frac {\sqrt {21} x}{3}} \]