Internal problem ID [14587]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+12 y^{\prime }+37 y={\mathrm e}^{-6 t} \csc \left (t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)+12*diff(y(t),t)+37*y(t)=exp(-6*t)*csc(t),y(t), singsol=all)
\[ y \left (t \right ) = -\left (\sin \left (t \right ) \ln \left (\csc \left (t \right )\right )+\left (-c_{1} +t \right ) \cos \left (t \right )-\sin \left (t \right ) c_{2} \right ) {\mathrm e}^{-6 t} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 30
DSolve[y''[t]+12*y'[t]+37*y[t]==Exp[-6*t]*Csc[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-6 t} ((-t+c_2) \cos (t)+\sin (t) (\log (\sin (t))+c_1)) \]