Internal problem ID [11469]
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 2.3.1 Nonhomogeneous Equations:
Undetermined Coefficients. Exercises page 110
Problem number: 2(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }-4 x=\cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(x(t),t$2)-4*x(t)=cos(2*t),x(t), singsol=all)
\[ x \left (t \right ) = c_{2} {\mathrm e}^{2 t}+{\mathrm e}^{-2 t} c_{1} -\frac {\cos \left (2 t \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 30
DSolve[x''[t]-4*x[t]==Cos[2*t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\frac {1}{8} \cos (2 t)+c_1 e^{2 t}+c_2 e^{-2 t} \]