Internal problem ID [262]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {m x^{\prime \prime }+k x=F_{0} \cos \left (\omega t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 60
dsolve(m*diff(x(t),t$2)+k*x(t)=F__0*cos(omega*t),x(t), singsol=all)
\[ x \left (t \right ) = \frac {c_{1} \left (-m \,\omega ^{2}+k \right ) \cos \left (\frac {\sqrt {k}\, t}{\sqrt {m}}\right )+c_{2} \left (-m \,\omega ^{2}+k \right ) \sin \left (\frac {\sqrt {k}\, t}{\sqrt {m}}\right )+F_{0} \cos \left (\omega t \right )}{-m \,\omega ^{2}+k} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 54
DSolve[m*x''[t]+k*x[t]==F0*Cos[omega*t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {\text {F0} \cos (\omega t)}{k-m \omega ^2}+c_1 \cos \left (\frac {\sqrt {k} t}{\sqrt {m}}\right )+c_2 \sin \left (\frac {\sqrt {k} t}{\sqrt {m}}\right ) \]