Internal problem ID [4640]
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]]
\[ \boxed {y^{\prime \prime }+y=\csc \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)=csc(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )-\ln \left (\csc \left (x \right )\right ) \sin \left (x \right )-x \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 24
DSolve[y''[x]+y[x]==Csc[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (-x+c_1) \cos (x)+\sin (x) (\log (\sin (x))+c_2) \]