29.7.25 problem 200

Internal problem ID [4800]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 200
Date solved : Monday, January 27, 2025 at 09:39:50 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

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

\[ y \left (x \right ) = -2 \arctan \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.352 (sec). Leaf size: 31

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

\begin{align*} y(x)\to 2 x \arctan (-\log (x)+c_1) \\ y(x)\to -\pi x \\ y(x)\to \pi x \\ \end{align*}