32.1.7 problem First order with homogeneous Coefficients. Exercise 7.8, page 61

Internal problem ID [5777]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number : First order with homogeneous Coefficients. Exercise 7.8, page 61
Date solved : Monday, January 27, 2025 at 01:17:07 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \operatorname {RootOf}\left (\textit {\_Z} x c_{1} \sin \left (\textit {\_Z} \right )-1\right ) x \]

✓ Solution by Mathematica

Time used: 0.266 (sec). Leaf size: 27

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

\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}\right )+\log \left (\sin \left (\frac {y(x)}{x}\right )\right )=-\log (x)+c_1,y(x)\right ] \]