Internal problem ID [2629]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.1
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve((y(x)*sin(x/y(x))+x*cos(x/y(x))-1)+(x*sin(x/y(x))-x^2/y(x)*cos(x/y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{\RootOf \left (x^{2} \sin \left (\textit {\_Z} \right )+\textit {\_Z} c_{1}-x \textit {\_Z} \right )} \]
✓ Solution by Mathematica
Time used: 0.396 (sec). Leaf size: 20
DSolve[(y[x]*Sin[x/y[x]]+x*Cos[x/y[x]]-1)+(x*Sin[x/y[x]]-x^2/y[x]*Cos[x/y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x-x y(x) \sin \left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]