74.11.9 problem 21

Internal problem ID [16259]
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 : 21
Date solved : Tuesday, January 28, 2025 at 08:58:58 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

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

\[ y = \frac {\left (8 c_{1} +1\right ) \cos \left (2 t \right )}{8}+\frac {\left (2 t +8 c_{2} \right ) \sin \left (2 t \right )}{8}+\frac {t}{4} \]

✓ Solution by Mathematica

Time used: 0.730 (sec). Leaf size: 78

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

\[ y(t)\to \cos (2 t) \int _1^t-\frac {1}{2} (\cos (2 K[1])+K[1]) \sin (2 K[1])dK[1]+\sin (2 t) \int _1^t\frac {1}{2} \cos (2 K[2]) (\cos (2 K[2])+K[2])dK[2]+c_1 \cos (2 t)+c_2 \sin (2 t) \]