Internal problem ID [2248]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\omega ^{2} y-\frac {F_{0} \cos \left (\omega t \right )}{m}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+omega^2*y(t)=F__0/m*cos(omega*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {F_{0} \sin \left (\omega t \right ) t +2 \cos \left (\omega t \right ) m \omega }{2 m \omega } \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 26
DSolve[{y''[t]+\[Omega]^2*y[t]==F0/m*Cos[\[Omega]*t],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\text {F0} t \sin (t \omega )}{2 m \omega }+\cos (t \omega ) \\ \end{align*}