66.2.4 problem Problem 4

Internal problem ID [13903]
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 : Tuesday, January 28, 2025 at 06:08:04 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+y(x)=1/sin(x)^3,y(x), singsol=all)
 

\[ y = \left (c_{1} +\cot \left (x \right )\right ) \cos \left (x \right )+\sin \left (x \right ) c_{2} -\frac {\csc \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 25

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

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