Internal problem ID [12224]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 186.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x \cos \left (\frac {y}{x}\right ) y^{\prime }-y \cos \left (\frac {y}{x}\right )=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(x*cos( y(x)/x)*diff(y(x),x)=y(x)*cos( y(x)/x) - x,y(x), singsol=all)
\[ y \left (x \right ) = -\arcsin \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.628 (sec). Leaf size: 15
DSolve[x*Cos[ y[x]/x]*y'[x]==y[x]*Cos[ y[x]/x] - x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \arcsin (-\log (x)+c_1) \]