Internal problem ID [14584]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+50 y={\mathrm e}^{-t} \csc \left (7 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+50*y(t)=exp(-t)*csc(7*t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\left (\frac {\sin \left (7 t \right ) \ln \left (\csc \left (7 t \right )\right )}{7}+\left (t -7 c_{1} \right ) \cos \left (7 t \right )-7 \sin \left (7 t \right ) c_{2} \right ) {\mathrm e}^{-t}}{7} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 42
DSolve[y''[t]+2*y'[t]+50*y[t]==Exp[-t]*Csc[7*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{49} e^{-t} (\sin (7 t) (\log (\sin (7 t))+49 c_1)-7 (t-7 c_2) \cos (7 t)) \]