64.10.7 problem 7

Internal problem ID [13342]
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 : 7
Date solved : Monday, March 31, 2025 at 07:51:57 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-8*diff(y(x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{4 x} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-8*D[y[x],x]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{4 x} (c_2 x+c_1) \]

✓ Sympy. Time used: 0.143 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - 8*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{4 x} \]