72.5.22 problem 9

Internal problem ID [14629]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number : 9
Date solved : Thursday, March 13, 2025 at 04:11:01 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1+\cos \left (y\right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 10

ode:=diff(y(t),t) = 1+cos(y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = 2 \arctan \left (t +c_{1} \right ) \]

✓ Mathematica. Time used: 0.243 (sec). Leaf size: 35

ode=D[y[t],t]==1+cos[y[t]]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\cos (K[1])+1}dK[1]\&\right ][t+c_1] \\ y(t)\to \cos ^{(-1)}(-1) \\ \end{align*}

✓ Sympy. Time used: 0.227 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = - 2 \operatorname {atan}{\left (C_{1} - t \right )} \]