Internal problem ID [12194]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 42.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x=\cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(x(t),t$4)+2*diff(x(t),t$2)+x(t)=cos(t),x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left (8 c_{3} t -t^{2}+8 c_{1} +2\right ) \cos \left (t \right )}{8}+\left (\left (c_{4} +\frac {3}{8}\right ) t +c_{2} \right ) \sin \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 43
DSolve[x''''[t]+2*x''[t]+x[t]==Cos[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \left (-\frac {t^2}{8}+c_2 t+\frac {5}{16}+c_1\right ) \cos (t)+\frac {1}{4} (t+4 c_4 t+4 c_3) \sin (t) \]