Internal problem ID [14917]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 5. Applications of Higher Order Equations. Exercises 5.3, page 249
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+\frac {x^{\prime }}{10}+x=3 \cos \left (2 t \right )} \] 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: 46
dsolve([diff(x(t),t$2)+1/10*diff(x(t),t)+x(t)=3*cos(2*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {125 \,{\mathrm e}^{-\frac {t}{20}} \sqrt {399}\, \sin \left (\frac {\sqrt {399}\, t}{20}\right )}{30058}+\frac {225 \,{\mathrm e}^{-\frac {t}{20}} \cos \left (\frac {\sqrt {399}\, t}{20}\right )}{226}-\frac {225 \cos \left (2 t \right )}{226}+\frac {15 \sin \left (2 t \right )}{226} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 74
DSolve[{x''[t]+1/10*x'[t]+x[t]==3*Cos[2*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\frac {5 e^{-t/20} \left (-399 e^{t/20} \sin (2 t)+25 \sqrt {399} \sin \left (\frac {\sqrt {399} t}{20}\right )+5985 e^{t/20} \cos (2 t)-5985 \cos \left (\frac {\sqrt {399} t}{20}\right )\right )}{30058} \]