72.5.23 problem 10

Internal problem ID [14630]
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 : 10
Date solved : Thursday, March 13, 2025 at 04:11:03 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.039 (sec). Leaf size: 9

ode:=diff(y(t),t) = tan(y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \arcsin \left (c_{1} {\mathrm e}^{t}\right ) \]

✓ Mathematica. Time used: 35.18 (sec). Leaf size: 17

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

\begin{align*} y(t)\to \arcsin \left (e^{t+c_1}\right ) \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.272 (sec). Leaf size: 19

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

\[ \left [ y{\left (t \right )} = \pi - \operatorname {asin}{\left (C_{1} e^{t} \right )}, \ y{\left (t \right )} = \operatorname {asin}{\left (C_{1} e^{t} \right )}\right ] \]