60.1.123 problem 124

Internal problem ID [10137]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 124
Date solved : Monday, January 27, 2025 at 06:29:33 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.373 (sec). Leaf size: 31

DSolve[x*D[y[x],x] + x*Cos[y[x]/x] - 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*}