64.10.32 problem 32

Internal problem ID [13367]
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 : 32
Date solved : Monday, March 31, 2025 at 07:52:29 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 14

ode:=9*diff(diff(y(x),x),x)-6*diff(y(x),x)+y(x) = 0; 
ic:=y(0) = 3, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {x}{3}} \left (3-2 x \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=9*D[y[x],{x,2}]-6*D[y[x],x]+y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{x/3} (3-2 x) \]

✓ Sympy. Time used: 0.162 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 6*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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