76.15.15 problem 16

Internal problem ID [17656]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 10:48:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 43

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

\[ y = \frac {\left (\left (t +6 c_{1} \right ) {\mathrm e}^{4 t}+6 c_{2} {\mathrm e}^{t}-\frac {\cosh \left (3 t \right ) {\mathrm e}^{t}}{3}-\frac {\sinh \left (3 t \right ) {\mathrm e}^{t}}{3}+\frac {3}{4}\right ) {\mathrm e}^{-2 t}}{6} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 39

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

\[ y(t)\to \frac {1}{72} e^{-2 t} \left (72 c_1 e^t+4 e^{4 t} (3 t-1+18 c_2)+9\right ) \]