Internal problem ID [3925]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\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 {gather*}
✓ Solution by Maple
Time used: 0.093 (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)
\[ y \relax (x ) = \RootOf \left (\textit {\_Z} x c_{1} \sin \left (\textit {\_Z} \right )-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.275 (sec). Leaf size: 27
DSolve[y[x]/x*Cos[y[x]/x]-(x/y[x]*Sin[y[x]/x]+Cos[y[x]/x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}\right )+\log \left (\sin \left (\frac {y(x)}{x}\right )\right )=-\log (x)+c_1,y(x)\right ] \]