62.3.6 problem Ex 6

Internal problem ID [12812]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
Problem number : Ex 6
Date solved : Tuesday, January 28, 2025 at 04:24:18 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 11

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

\[ y = \arcsin \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 24

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\cos (K[1])dK[1]=\log (x)+c_1,y(x)\right ] \]