Internal problem ID [12167]
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]]
\[ \boxed {y^{\prime \prime }+y=\frac {1}{\sin \left (x \right )^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+y(x)=1/sin(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} +\cot \left (x \right )\right ) \cos \left (x \right )+\sin \left (x \right ) c_{2} -\frac {\csc \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 25
DSolve[y''[x]+y[x]==1/Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\csc (x)}{2}+c_2 \sin (x)+\cos (x) (\cot (x)+c_1) \]