Internal problem ID [14453]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=2 \cos \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve([diff(y(t),t$2)+y(t)=2*cos(t),y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (t \right )+\cos \left (t \right )+\sin \left (t \right ) t \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 14
DSolve[{y''[t]+y[t]==2*Cos[t],{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to (t+1) \sin (t)+\cos (t) \]