83.38.5 problem 5

Internal problem ID [19393]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (C) at page 133
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:12:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\sin \left (x \right )^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.074 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-cot(x)*diff(y(x),x)-sin(x)^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sinh \left (\cos \left (x \right )\right )+c_2 \cosh \left (\cos \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 21

ode=D[y[x],{x,2}]-Cot[x]*D[y[x],x]-Sin[x]^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cosh (\cos (x))-i c_2 \sinh (\cos (x)) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*sin(x)**2 + Derivative(y(x), (x, 2)) - Derivative(y(x), x)/tan(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-y(x)*sin(x)**2 + Derivative(y(x), (x, 2)))*tan(x) + Derivative(y(x), x) cannot be solved by the factorable group method