74.10.30 problem 30

Internal problem ID [16164]
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 : 30
Date solved : Monday, March 31, 2025 at 02:45:43 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.093 (sec). Leaf size: 20

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

\[ y = \frac {2 \sqrt {3}\, {\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right )}{3} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 30

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

\[ y(t)\to \frac {2 e^{t/2} \sin \left (\frac {\sqrt {3} t}{2}\right )}{\sqrt {3}} \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 26

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

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