68.10.42 problem 41

Internal problem ID [17534]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 41
Date solved : Thursday, October 02, 2025 at 02:25:11 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.050 (sec). Leaf size: 5

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+5*y(t) = 0; 
ic:=[y(0) = 0, D(y)(1/2*Pi) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 3

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

\[ y{\left (t \right )} = 0 \]