Internal problem ID [2065]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve((y(x)*cos(x/y(x)))-(y(x)+x*cos(x/y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{\operatorname {RootOf}\left (-\textit {\_Z} \,{\mathrm e}^{\sin \left (\textit {\_Z} \right )}+c_{1} x \right )} \]
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 28
DSolve[(y[x]*Cos[x/y[x]])-(y[x]+x*Cos[x/y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}\right )-\sin \left (\frac {x}{y(x)}\right )=-\log (x)+c_1,y(x)\right ] \]