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]]
\[ \boxed {x^{\prime \prime }+25 x=90 \cos \left (4 t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 90] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ x \left (t \right ) = 18 \sin \left (5 t \right )-10 \cos \left (5 t \right )+10 \cos \left (4 t \right ) \]
✓ Solution by Mathematica
Time used: 0.019 (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]
\[ x(t)\to 2 (9 \sin (5 t)+5 \cos (4 t)-5 \cos (5 t)) \]