83.43.2 problem Ex 3 page 7

Internal problem ID [19439]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 3 page 7
Date solved : Monday, March 31, 2025 at 07:13:49 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 11

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

\[ y = \arccos \left (\frac {\csc \left (x \right )}{c_1}\right ) \]

✓ Mathematica. Time used: 5.513 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to \arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}

✓ Sympy. Time used: 0.521 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-tan(x)*Derivative(y(x), x) + 1/tan(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (\frac {C_{1}}{\sin {\left (x \right )}} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (\frac {C_{1}}{\sin {\left (x \right )}} \right )}\right ] \]