58.4.11 problem 11

Internal problem ID [14581]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:42:51 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 10

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

\[ y = \arcsin \left (c_1 x \right ) x \]

✓ Mathematica. Time used: 1.911 (sec). Leaf size: 19

ode=(x*Tan[y[x]/x]+y[x])- x*D[y[x],x]==0; 
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: 0.746 (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)
 

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