29.8.4 problem 209

Internal problem ID [4809]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 209
Date solved : Sunday, March 30, 2025 at 03:59:18 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 12.191 (sec). Leaf size: 19

ode=x D[y[x],x]+Tan[y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.338 (sec). Leaf size: 15

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

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