Internal problem ID [10819]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-\frac {1}{\sin \left (x \right )^{3}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+y(x)=1/sin(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )+\cot \left (x \right ) \cos \left (x \right )-\frac {\csc \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 24
DSolve[y''[x]+y[x]==1/Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\csc (x)}{2}+c_1 \cos (x)+(-1+c_2) \sin (x) \\ \end{align*}