Internal problem ID [260]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+100 x-225 \cos \left (5 t \right )-300 \sin \left (5 t \right )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 375, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 29
dsolve([diff(x(t),t$2)+100*x(t)=225*cos(5*t)+300*sin(5*t),x(0) = 375, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = 744 \left (\cos ^{2}\left (5 t \right )\right )+\left (-4 \sin \left (5 t \right )+3\right ) \cos \left (5 t \right )+4 \sin \left (5 t \right )-372 \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 30
DSolve[{x''[t]+100*x[t]==225*Cos[5*t]+300*Sin[5*t],{x[0]==375,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 4 \sin (5 t)-2 \sin (10 t)+3 \cos (5 t)+372 \cos (10 t) \\ \end{align*}