74.8.33 problem 33

Internal problem ID [16169]
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 : Tuesday, January 28, 2025 at 08:55:37 AM
CAS classification : [_exact]

\begin{align*} \sin \left (y\right )-y \cos \left (t \right )+\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*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([(sin(y(t))-y(t)*cos(t))+(t*cos(y(t))-sin(t))*diff(y(t),t)=0,y(Pi) = 0],y(t), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 6

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

\[ y(t)\to 0 \]