Internal problem ID [14916]
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: 22 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x=\cos \left (\frac {7 t}{10}\right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+x(t)=cos(7/10*t),x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \right )-\frac {100 \cos \left (t \right )}{51}+\frac {100 \cos \left (\frac {7 t}{10}\right )}{51} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 24
DSolve[{x''[t]+x[t]==Cos[7/10*t],{x[0]==0,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \sin (t)+\frac {100}{51} \cos \left (\frac {7 t}{10}\right )-\frac {100 \cos (t)}{51} \]