65.6.5 problem 12.1 (v)

Internal problem ID [13683]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (v)
Date solved : Monday, March 31, 2025 at 08:08:51 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=13\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 5

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t) = 0; 
ic:=y(0) = 13, D(y)(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = 13 \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 6

ode=D[y[t],{t,2}]-4*D[y[t],t]==0; 
ic={y[0]==13,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 13 \]

✓ Sympy. Time used: 0.136 (sec). Leaf size: 3

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 13, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 13 \]