74.11.25 problem 37

Internal problem ID [16275]
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 : 37
Date solved : Tuesday, January 28, 2025 at 09:00:04 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=-32 t^{2} \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(diff(y(t),t$2)+4*diff(y(t),t)+4*y(t)=-32*t^2*cos(2*t),y(t), singsol=all)
 

\[ y = \left (3-4 t \right ) \cos \left (2 t \right )+\left (c_{1} t +c_{2} \right ) {\mathrm e}^{-2 t}-4 t \sin \left (2 t \right ) \left (t -1\right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 44

DSolve[D[y[t],{t,2}]+4*D[y[t],t]+4*y[t]==-32*t^2*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to (3-4 t) \cos (2 t)+e^{-2 t} \left (-4 e^{2 t} (t-1) t \sin (2 t)+c_2 t+c_1\right ) \]