74.12.19 problem 19

Internal problem ID [16326]
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 : 19
Date solved : Tuesday, January 28, 2025 at 09:04:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=2 \sinh \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(diff(y(t),t$2)-y(t)=2*sinh(t),y(t), singsol=all)
 

\[ y = \frac {\left (2 t +4 c_{2} \right ) {\mathrm e}^{-t}}{4}+\frac {{\mathrm e}^{t} \left (t +2 c_{1} -\frac {1}{2}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 38

DSolve[D[y[t],{t,2}]-y[t]==2*Sinh[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} e^{-t} \left (2 t+e^{2 t} (2 t-1+4 c_1)+1+4 c_2\right ) \]