Internal problem ID [2004]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+\omega _{0}^{2} x-a \cos \left (\omega 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: 0.032 (sec). Leaf size: 28
dsolve([diff(x(t),t$2)+ (omega__0)^2*x(t)=a*cos(omega*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = \frac {a \left (\cos \left (\omega _{0} t \right )-\cos \left (\omega t \right )\right )}{\omega ^{2}-\omega _{0}^{2}} \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 33
DSolve[{x''[t]+(Subscript[\[Omega],0])^2*x[t]==a*Cos[\[Omega]*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {a \left (\cos \left (t \omega _0\right )-\cos (t \omega )\right )}{\omega ^2-\omega _0^2} \\ \end{align*}