Internal problem ID [14060]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x=\cos \left (t \right ) t -\cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(x(t),t$2)+x(t)=t*cos(t)-cos(t),x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left (t^{2}+4 c_{2} -2 t -1\right ) \sin \left (t \right )}{4}+\frac {\cos \left (t \right ) \left (t +4 c_{1} -2\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 38
DSolve[x''[t]+x[t]==t*Cos[t]-Cos[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{8} \left (\left (2 t^2-4 t-1+8 c_2\right ) \sin (t)+2 (t-2+4 c_1) \cos (t)\right ) \]