30.12.34 problem 44

Internal problem ID [7626]
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 : 44
Date solved : Tuesday, September 30, 2025 at 04:55:05 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=3 \\ y^{\prime \prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 11

ode:=diff(diff(diff(y(t),t),t),t)-2*diff(diff(y(t),t),t)-diff(y(t),t)+2*y(t) = 0; 
ic:=[y(0) = 2, D(y)(0) = 3, (D@@2)(y)(0) = 5]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = {\mathrm e}^{2 t}+{\mathrm e}^{t} \]

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

ode=D[y[t],{t,3}]-2*D[y[t],{t,2}]-D[y[t],{t,1}]+2*y[t]==0; 
ic={y[0]==2,Derivative[1][y][0] ==3,Derivative[2][y][0] ==5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \left (e^t+1\right ) \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) - Derivative(y(t), t) - 2*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 3, Subs(Derivative(y(t), (t, 2)), t, 0): 5} 
dsolve(ode,func=y(t),ics=ics)
 

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