72.16.22 problem 23

Internal problem ID [14839]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 23
Date solved : Thursday, March 13, 2025 at 04:21:05 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=10 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 25

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+10*y(t) = 10; 
ic:=y(0) = 0, D(y)(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = 1+\frac {\left (-\sin \left (3 t \right )-3 \cos \left (3 t \right )\right ) {\mathrm e}^{-t}}{3} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 32

ode=D[y[t],{t,2}]+2*D[y[t],t]+10*y[t]==10; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{3} e^{-t} \left (3 e^t-\sin (3 t)-3 \cos (3 t)\right ) \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(10*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 10,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (- \frac {\sin {\left (3 t \right )}}{3} - \cos {\left (3 t \right )}\right ) e^{- t} + 1 \]