69.20.17 problem 656

Internal problem ID [18438]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 656
Date solved : Thursday, October 02, 2025 at 03:11:54 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 48

ode:=diff(diff(y(x),x),x)+y(x) = 1/(sin(x)^5*cos(x))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x \right ) c_2 +\cos \left (x \right ) c_1 +\int \frac {\cos \left (x \right )}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}d x \sin \left (x \right )-\int \frac {\sin \left (x \right )}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}d x \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 35

ode=D[y[x],{x,2}]+y[x]==1/Sqrt[Sin[x]^5*Cos[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \cos (x)+c_2 \sin (x)+\frac {4}{3} \csc ^8(x) \left (\sin ^5(x) \cos (x)\right )^{3/2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)) - 1/sqrt(sin(x)**5*cos(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out