27.1.5 problem 5

Internal problem ID [4299]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.1
Problem number : 5
Date solved : Monday, January 27, 2025 at 08:50:52 AM
CAS classification : [_exact]

\begin{align*} 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{align*}

✓ Solution by Maple

Time used: 0.026 (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)
 

\[ y \left (x \right ) = \frac {x}{\operatorname {RootOf}\left (x^{2} \sin \left (\textit {\_Z} \right )+c_{1} \textit {\_Z} -x \textit {\_Z} \right )} \]

✓ Solution by Mathematica

Time used: 0.398 (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]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x-x y(x) \sin \left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]