Internal problem ID [14868]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\csc \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(t),t$2)+y(t)=csc(t),y(t), singsol=all)
\[ y \left (t \right ) = -\sin \left (t \right ) \ln \left (\csc \left (t \right )\right )+\left (-t +c_{1} \right ) \cos \left (t \right )+\sin \left (t \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 24
DSolve[y''[t]+y[t]==Csc[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to (-t+c_1) \cos (t)+\sin (t) (\log (\sin (t))+c_2) \]