72.7.21 problem 21

Internal problem ID [14683]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 21
Date solved : Thursday, March 13, 2025 at 04:14:22 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} v^{\prime }+\frac {2 v}{5}&=3 \cos \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(v(t),t)+2/5*v(t) = 3*cos(2*t); 
dsolve(ode,v(t), singsol=all);
 

\[ v = \frac {15 \cos \left (2 t \right )}{52}+\frac {75 \sin \left (2 t \right )}{52}+{\mathrm e}^{-\frac {2 t}{5}} c_{1} \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 38

ode=D[ v[t],t]+4/10*v[t]==3*Cos[2*t]; 
ic={}; 
DSolve[{ode,ic},v[t],t,IncludeSingularSolutions->True]
 

\[ v(t)\to e^{-2 t/5} \left (\int _1^t3 e^{\frac {2 K[1]}{5}} \cos (2 K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.164 (sec). Leaf size: 27

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

\[ v{\left (t \right )} = C_{1} e^{- \frac {2 t}{5}} + \frac {75 \sin {\left (2 t \right )}}{52} + \frac {15 \cos {\left (2 t \right )}}{52} \]