72.17.4 problem 4

Internal problem ID [14861]
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 4.2 page 412
Problem number : 4
Date solved : Thursday, March 13, 2025 at 05:13:46 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=2 \sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)+2*y(t) = 2*sin(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -c_{1} {\mathrm e}^{-2 t}-\frac {3 \cos \left (t \right )}{5}+\frac {\sin \left (t \right )}{5}+c_{2} {\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 32

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

\[ y(t)\to \frac {1}{5} \left (\sin (t)-3 \cos (t)+5 e^{-2 t} \left (c_2 e^t+c_1\right )\right ) \]

✓ Sympy. Time used: 0.202 (sec). Leaf size: 26

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

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{- t} + \frac {\sin {\left (t \right )}}{5} - \frac {3 \cos {\left (t \right )}}{5} \]