23.1.218 problem 214

Internal problem ID [4825]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 214
Date solved : Tuesday, September 30, 2025 at 08:43:09 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

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

\[ y = x \arcsin \left (\frac {1}{x c_1}\right ) \]

✓ Mathematica. Time used: 8.39 (sec). Leaf size: 21

ode=x*D[y[x],x]==y[x]-x*Tan[y[x]/x]; 
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: 0.806 (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)
 

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