Internal problem ID [14913]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 5. Applications of Higher Order Equations. Exercises 5.3, page 249
Problem number: 21 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x=\cos \left (t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([diff(x(t),t$2)+x(t)=cos(t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\sin \left (t \right ) t}{2} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 12
DSolve[{x''[t]+x[t]==Cos[t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{2} t \sin (t) \]