74.6.3 problem 3

Internal problem ID [15955]
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 : Monday, March 31, 2025 at 02:16:08 PM
CAS classification : [_separable]

\begin{align*} y \cos \left (t y\right )+t \cos \left (t y\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: 0.028 (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: 0.259 (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)
 

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