Internal problem ID [14318]
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: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _dAlembert]
\[ \boxed {2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 12
dsolve((2*t*sin(y(t)/t)-y(t)*cos(y(t)/t))+t*cos(y(t)/t)*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \arcsin \left (\frac {c_{1}}{t^{2}}\right ) t \]
✓ Solution by Mathematica
Time used: 14.41 (sec). Leaf size: 21
DSolve[(2*t*Sin[y[t]/t]-y[t]*Cos[y[t]/t])+t*Cos[y[t]/t]*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t \arcsin \left (\frac {e^{c_1}}{t^2}\right ) \\ y(t)\to 0 \\ \end{align*}