74.6.29 problem 30

Internal problem ID [16052]
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
Date solved : Tuesday, January 28, 2025 at 08:31:49 AM
CAS classification : [[_homogeneous, `class A`], _exact, _dAlembert]

\begin{align*} 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 \end{align*}

✓ Solution by Maple

Time used: 0.071 (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)
 

\[ y = \arcsin \left (\frac {c_{1}}{t^{2}}\right ) t \]

✓ Solution by Mathematica

Time used: 12.838 (sec). Leaf size: 21

DSolve[(2*t*Sin[y[t]/t]-y[t]*Cos[y[t]/t])+t*Cos[y[t]/t]*D[y[t],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*}