74.18.38 problem 44

Internal problem ID [16595]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 44
Date solved : Tuesday, January 28, 2025 at 09:12:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 24

dsolve([diff(y(t),t$2)+9*y(t)=sin(3*t),y(0) = 6, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {\sin \left (3 t \right )}{18}+6 \cos \left (3 t \right )-\frac {t \cos \left (3 t \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 102

DSolve[{D[y[t],{t,2}]+9*y[t]==Sin[3*t],{y[0]==6,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\sin (3 t) \int _1^0\frac {1}{6} \sin (6 K[2])dK[2]+\sin (3 t) \int _1^t\frac {1}{6} \sin (6 K[2])dK[2]+\cos (3 t) \left (-\int _1^0-\frac {1}{3} \sin ^2(3 K[1])dK[1]\right )+\cos (3 t) \int _1^t-\frac {1}{3} \sin ^2(3 K[1])dK[1]+6 \cos (3 t) \]