Internal problem ID [14865]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\sin \left (3 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = \frac {\sin \left (3 t \right )}{18}+6 \cos \left (3 t \right )-\frac {\cos \left (3 t \right ) t}{6} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 23
DSolve[{y''[t]+9*y[t]==Sin[3*t],{y[0]==6,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{18} (\sin (3 t)-3 (t-36) \cos (3 t)) \]