74.22.1 problem 1

Internal problem ID [16648]
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 : Tuesday, January 28, 2025 at 09:16:13 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 16

dsolve([diff(x(t),t)=6,diff(y(t),t)=cos(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= 6 t +c_{2} \\ y &= \sin \left (t \right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[{D[x[t],t]==6,D[y[t],t]==Cos[t]},{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*}