68.6.3 problem 3

Internal problem ID [17313]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 3
Date solved : Thursday, October 02, 2025 at 02:02:07 PM
CAS classification : [_separable]

\begin{align*} y \cos \left (y t \right )+t \cos \left (y t \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

ode:=y(t)*cos(t*y(t))+t*cos(t*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {\pi }{2 t} \\ y &= -\frac {c_1}{t} \\ \end{align*}

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 59

ode=y[t]*Cos[t*y[t]]+t*Cos[t*y[t]]*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {\pi }{2 t}\\ y(t)&\to \frac {\pi }{2 t}\\ y(t)&\to \frac {c_1}{t}\\ y(t)&\to -\frac {\pi }{2 t}\\ y(t)&\to \frac {\pi }{2 t} \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 5

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

\[ y{\left (t \right )} = \frac {C_{1}}{t} \]