74.6.24 problem 25

Internal problem ID [15976]
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 : 25
Date solved : Monday, March 31, 2025 at 02:18:10 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} 1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=1-y(t)^2*cos(t*y(t))+(t*y(t)*cos(t*y(t))+sin(t*y(t)))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(1-y[t]^2*Cos[t*y[t]])+(t*y[t]*Cos[t*y[t]]+Sin[t*y[t]])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t*y(t)*cos(t*y(t)) + sin(t*y(t)))*Derivative(y(t), t) - y(t)**2*cos(t*y(t)) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out