60.1.124 problem 125

Internal problem ID [10138]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 125
Date solved : Monday, January 27, 2025 at 06:29:37 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 12.398 (sec). Leaf size: 21

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

\begin{align*} y(x)\to x \arcsin \left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}