74.12.9 problem 9

Internal problem ID [16316]
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
Date solved : Tuesday, January 28, 2025 at 09:03:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = -\frac {\left (\frac {\sin \left (7 t \right ) \ln \left (\csc \left (7 t \right )\right )}{7}+\left (t -7 c_{1} \right ) \cos \left (7 t \right )-7 \sin \left (7 t \right ) c_{2} \right ) {\mathrm e}^{-t}}{7} \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 42

DSolve[D[y[t],{t,2}]+2*D[y[t],t]+50*y[t]==Exp[-t]*Csc[7*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{49} e^{-t} (\sin (7 t) (\log (\sin (7 t))+49 c_1)-7 (t-7 c_2) \cos (7 t)) \]