60.3.64 problem 1069

Internal problem ID [11060]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1069
Date solved : Sunday, March 30, 2025 at 07:41:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 1.998 (sec). Leaf size: 18

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

\[ y(x)\to c_1 \cos (\cos (x))+c_2 \sin (\cos (x)) \]

✗ 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