Internal problem ID [11477]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.3.2 Resonance Exercises page
114
Problem number: 7(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+3025 x=\cos \left (45 t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+(55)^2*x(t)=cos(45*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\cos \left (55 t \right )}{1000}+\frac {\cos \left (45 t \right )}{1000} \]
✓ Solution by Mathematica
Time used: 0.338 (sec). Leaf size: 36
DSolve[{x''[t]+55^2*x[t]==Cos[45*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{250} \sin ^2(5 t) (\cos (5 t)+\cos (15 t)+\cos (25 t)+\cos (35 t)+\cos (45 t)) \]