Internal problem ID [4132]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.10, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\csc \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+y(x)=csc(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}-\ln \left (\frac {1}{\sin \relax (x )}\right ) \sin \relax (x )-x \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 24
DSolve[y''[x]+y[x]==Csc[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (-x+c_1) \cos (x)+\sin (x) (\log (\sin (x))+c_2) \\ \end{align*}