88.1.2 problem 16

Internal problem ID [23945]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 6
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:46:42 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

ode:=diff(y(t),t) = cos(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t}{2}+c_1 +\frac {\sin \left (2 t \right )}{4} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 20

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

\begin{align*} y(t)&\to \frac {1}{2} (t+\sin (t) \cos (t)+2 c_1) \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = C_{1} + \frac {t}{2} + \frac {\sin {\left (t \right )} \cos {\left (t \right )}}{2} \]