72.6.4 problem 4

Internal problem ID [14658]
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 1.8 page 121
Problem number : 4
Date solved : Monday, March 31, 2025 at 12:51:45 PM
CAS classification : [[_linear, `class A`]]

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

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

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

\[ y = -\frac {\cos \left (2 t \right )}{4}-\frac {\sin \left (2 t \right )}{4}+{\mathrm e}^{2 t} c_1 \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 33

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

\[ y(t)\to e^{2 t} \left (\int _1^te^{-2 K[1]} \sin (2 K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.139 (sec). Leaf size: 22

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

\[ y{\left (t \right )} = C_{1} e^{2 t} - \frac {\sin {\left (2 t \right )}}{4} - \frac {\cos {\left (2 t \right )}}{4} \]