74.18.41 problem 47

Internal problem ID [16598]
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
Date solved : Tuesday, January 28, 2025 at 09:12:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\csc \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(diff(y(t),t$2)+y(t)=csc(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

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

\[ y(t)\to (-t+c_1) \cos (t)+\sin (t) (\log (\sin (t))+c_2) \]