40.2.6 problem 29

Internal problem ID [6584]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 29
Date solved : Monday, January 27, 2025 at 02:14:14 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

dsolve((x*sin(y(x)/x)-y(x)*cos(y(x)/x))+(x*cos(y(x)/x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = x \arcsin \left (\frac {1}{c_1 x}\right ) \]

✓ Solution by Mathematica

Time used: 12.493 (sec). Leaf size: 21

DSolve[(x*Sin[y[x]/x]-y[x]*Cos[y[x]/x])+(x*Cos[y[x]/x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \arcsin \left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}