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 : Tuesday, March 04, 2025 at 03:47:16 PM
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*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 19

ode:=y(x)*cos(x/y(x))-(y(x)+x*cos(x/y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=(y[x]*Cos[x/y[x]])-(y[x]+x*Cos[x/y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 3.334 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x*cos(x/y(x)) - y(x))*Derivative(y(x), x) + y(x)*cos(x/y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (y{\left (x \right )} \right )} = C_{1} + \sin {\left (\frac {x}{y{\left (x \right )}} \right )} \]