47.2.6 problem 6

Internal problem ID [7422]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 6
Date solved : Wednesday, March 05, 2025 at 04:29:30 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: 0.007 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 9.413 (sec). Leaf size: 19

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

✓ Sympy. Time used: 1.285 (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)
 

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