68.4.42 problem 42

Internal problem ID [17222]
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 : Thursday, October 02, 2025 at 01:58:48 PM
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*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 8

ode:=diff(y(t),t) = cos(t); 
ic:=[y(1/2*Pi) = -1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.025 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-cos(t) + Derivative(y(t), t),0) 
ics = {y(pi/2): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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