64.10.4 problem 4

Internal problem ID [13331]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 4
Date solved : Wednesday, March 05, 2025 at 09:48:13 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }-14 y^{\prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=3*diff(diff(y(x),x),x)-14*diff(y(x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} c_{1} +c_{2} {\mathrm e}^{-\frac {x}{3}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

ode=3*D[y[x],{x,2}]-14*D[y[x],x]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{-x/3}+c_2 e^{5 x} \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - 14*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {x}{3}} + C_{2} e^{5 x} \]