60.1.1 problem Problem 1

Internal problem ID [15129]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 1
Date solved : Thursday, October 02, 2025 at 10:03:19 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.039 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 2.726 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \arcsin \left (\frac {1}{2} c_1 \sec (x)\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.323 (sec). Leaf size: 19

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

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