Internal problem ID [14291]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(y(t)*cos(t*y(t))+t*cos(t*y(t))*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {\pi }{2 t} \\ y \left (t \right ) &= -\frac {c_{1}}{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 59
DSolve[y[t]*Cos[t*y[t]]+t*Cos[t*y[t]]*y'[t]==0,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*}