74.11.23 problem 35

Internal problem ID [16273]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 09:00:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 30

dsolve(diff(y(t),t$2)-9*y(t)=54*t*sin(2*t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-3 t} c_{2} +c_{1} {\mathrm e}^{3 t}-\frac {216 \cos \left (2 t \right )}{169}-\frac {54 \sin \left (2 t \right ) t}{13} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 40

DSolve[D[y[t],{t,2}]-9*y[t]==54*t*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{3 t}+c_2 e^{-3 t}-\frac {54}{169} (13 t \sin (2 t)+4 \cos (2 t)) \]