60.2.4 problem Problem 4

Internal problem ID [15184]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 4
Date solved : Thursday, October 02, 2025 at 10:06:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )^{3}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+y(x) = 1/sin(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 +\cot \left (x \right )\right ) \cos \left (x \right )+\sin \left (x \right ) c_2 -\frac {\csc \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 25

ode=D[y[x],{x,2}]+y[x]==1/Sin[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\csc (x)}{2}+c_2 \sin (x)+\cos (x) (\cot (x)+c_1) \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + Derivative(y(x), (x, 2)) - 1/sin(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )} + \frac {1}{2 \sin {\left (x \right )}} \]