30.12.15 problem 15

Internal problem ID [7607]
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 : 15
Date solved : Tuesday, September 30, 2025 at 04:54:52 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+3*y(t) = 0; 
ic:=[y(0) = 1, D(y)(0) = 1/3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{3 t}}{3}+\frac {4 \,{\mathrm e}^{t}}{3} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 19

ode=D[y[t],{t,2}]-4*D[y[t],t]+3*y[t]==0; 
ic={y[0]==1,Derivative[1][y][0] ==1/3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {1}{3} e^t \left (e^{2 t}-4\right ) \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 1/3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\frac {4}{3} - \frac {e^{2 t}}{3}\right ) e^{t} \]