Internal problem ID [11136]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 10.
Homogeneous equations. Page 15
Problem number: Ex 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve((x+y(x)*cos(y(x)/x))-x*cos(y(x)/x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.395 (sec). Leaf size: 13
DSolve[(x+y[x]*Cos[y[x]/x])-x*Cos[y[x]/x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \arcsin (\log (x)+c_1) \]