Internal problem ID [2757]
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]]
\[ \boxed {y^{\prime \prime }+\omega ^{2} y=\frac {F_{0} \cos \left (\omega t \right )}{m}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = \cos \left (\omega t \right )+\frac {F_{0} \sin \left (\omega t \right ) t}{2 \omega m} \]
✓ Solution by Mathematica
Time used: 0.082 (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]
\[ y(t)\to \frac {\text {F0} t \sin (t \omega )}{2 m \omega }+\cos (t \omega ) \]