30.12.20 problem 20

Internal problem ID [7612]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 04:54:55 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 16

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+4*y(t) = 0; 
ic:=[y(1) = 1, D(y)(1) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \left (2-t \right ) {\mathrm e}^{-2+2 t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 17

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

\begin{align*} y(t)&\to -e^{2 t-2} (t-2) \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(1): 1, Subs(Derivative(y(t), t), t, 1): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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