60.1.122 problem 125

Internal problem ID [10136]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 125
Date solved : Wednesday, March 05, 2025 at 08:33:10 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

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

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

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

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

ode=x*D[y[x],x] + x*Tan[y[x]/x] - y[x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 1.298 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = x \left (\pi - \operatorname {asin}{\left (\frac {C_{1}}{x} \right )}\right ), \ y{\left (x \right )} = x \operatorname {asin}{\left (\frac {C_{1}}{x} \right )}\right ] \]