15.8.33 problem 35

Internal problem ID [3036]
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
Date solved : Monday, January 27, 2025 at 07:10:51 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (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)
 

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

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 28

DSolve[(y[x]*Cos[x/y[x]])-(y[x]+x*Cos[x/y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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