Internal problem ID [10457]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 2, Second order linear equations. Section 2.3.2 Resonance Exercises page
114
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x-\cos \left (2 t \right )=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 27
dsolve([diff(x(t),t$2)+1/100*diff(x(t),t)+4*x(t)=cos(2*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {20000 \,{\mathrm e}^{-\frac {t}{200}} \sqrt {159999}\, \sin \left (\frac {\sqrt {159999}\, t}{200}\right )}{159999}+50 \sin \left (2 t \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x''[t]+1/100**x'[t]+4*x[t]==Cos[2*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
Not solved