74.22.1 problem 1

Internal problem ID [16577]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 1
Date solved : Monday, March 31, 2025 at 02:59:30 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=6\\ \frac {d}{d t}y \left (t \right )&=\cos \left (t \right ) \end{align*}

✓ Maple. Time used: 0.148 (sec). Leaf size: 16

ode:=[diff(x(t),t) = 6, diff(y(t),t) = cos(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= 6 t +c_2 \\ y \left (t \right ) &= \sin \left (t \right )+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 27

ode={D[x[t],t]==6,D[y[t],t]==Cos[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to 6 t+c_1 \\ y(t)\to \int _1^t\cos (K[1])dK[1]+c_2 \\ \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(Derivative(x(t), t) - 6,0),Eq(-cos(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = C_{1} + 6 t, \ y{\left (t \right )} = C_{2} + \sin {\left (t \right )}\right ] \]