Internal problem ID [261]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+25 x-90 \cos \left (4 t \right )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 0, x^{\prime }\relax (0) = 90] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(x(t),t$2)+25*x(t)=90*cos(4*t),x(0) = 0, D(x)(0) = 90],x(t), singsol=all)
\[ x \relax (t ) = -160 \left (\cos ^{5}\relax (t )\right )+\left (288 \sin \relax (t )+80\right ) \left (\cos ^{4}\relax (t )\right )+200 \left (\cos ^{3}\relax (t )\right )+\left (-216 \sin \relax (t )-80\right ) \left (\cos ^{2}\relax (t )\right )-50 \cos \relax (t )+18 \sin \relax (t )+10 \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 26
DSolve[{x''[t]+25*x[t]==90*Cos[4*t],{x[0]==0,x'[0]==90}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 2 (9 \sin (5 t)+5 \cos (4 t)-5 \cos (5 t)) \\ \end{align*}