Internal problem ID [258]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+9 x-10 \cos \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 0, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+9*x(t)=10*cos(2*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = -8 \left (\cos ^{3}\relax (t )\right )+6 \cos \relax (t )+4 \left (\cos ^{2}\relax (t )\right )-2 \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 18
DSolve[{x''[t]+9*x[t]==10*Cos[2*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 2 (\cos (2 t)-\cos (3 t)) \\ \end{align*}