74.4.42 problem 42

Internal problem ID [15935]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 42
Date solved : Tuesday, January 28, 2025 at 08:23:28 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 8

dsolve([diff(y(t),t)=cos(t),y(1/2*Pi) = -1],y(t), singsol=all)
 

\[ y = \sin \left (t \right )-2 \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 21

DSolve[{D[y[t],t]==Cos[t],{y[Pi/2]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _{\frac {\pi }{2}}^t\cos (K[1])dK[1]-1 \]