60.3.415 problem 1432

Internal problem ID [11411]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1432
Date solved : Sunday, March 30, 2025 at 08:21:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)-1/4*(-17*sin(x)^2-1)/sin(x)^2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \sinh \left (2 x \right )+c_2 \cosh \left (2 x \right )}{\sqrt {\sin \left (x \right )}} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 33

ode=D[y[x],{x,2}] == -1/4*(Csc[x]^2*(-1 - 17*Sin[x]^2)*y[x]) - Cot[x]*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{-2 x} \left (c_2 e^{4 x}+4 c_1\right )}{4 \sqrt {\sin (x)}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-17*sin(x)**2 - 1)*y(x)/(4*sin(x)**2) + Derivative(y(x), (x, 2)) + cos(x)*Derivative(y(x), x)/sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -((17*y(x) - 4*Derivative(y(x), (x, 2)))*sin(x)**2 + y(x))/(4*sin(x)*cos(x)) + Derivative(y(x), x) cannot be solved by the factorable group method