68.8.33 problem 33

Internal problem ID [17456]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 33
Date solved : Saturday, October 04, 2025 at 05:34:17 PM
CAS classification : [_exact]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 5

ode:=sin(y(t))-y(t)*cos(t)+(t*cos(y(t))-sin(t))*diff(y(t),t) = 0; 
ic:=[y(Pi) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 0 \end{align*}

✗ Sympy

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

Timed Out