74.12.12 problem 12

Internal problem ID [16319]
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
Date solved : Tuesday, January 28, 2025 at 09:03:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = -{\mathrm e}^{-6 t} \left (\sin \left (t \right ) \ln \left (\csc \left (t \right )\right )+\left (t -c_{1} \right ) \cos \left (t \right )-c_{2} \sin \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 30

DSolve[D[y[t],{t,2}]+12*D[y[t],t]+37*y[t]==Exp[-6*t]*Csc[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-6 t} ((-t+c_2) \cos (t)+\sin (t) (\log (\sin (t))+c_1)) \]