Internal problem ID [11726]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 16, Higher order linear equations with constant coefficients. Exercises page
153
Problem number: 16.1 (iii).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x=\sin \left (t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(x(t),t$4)-4*diff(x(t),t$3)+8*diff(x(t),t$2)-8*diff(x(t),t)+4*x(t)=sin(t),x(t), singsol=all)
\[ x \left (t \right ) = -\frac {3 \sin \left (t \right )}{25}+\frac {4 \cos \left (t \right )}{25}+c_{1} {\mathrm e}^{t} \cos \left (t \right )+c_{2} {\mathrm e}^{t} \sin \left (t \right )+c_{3} {\mathrm e}^{t} \cos \left (t \right ) t +c_{4} {\mathrm e}^{t} \sin \left (t \right ) t \]
✓ Solution by Mathematica
Time used: 0.258 (sec). Leaf size: 42
DSolve[x''''[t]-4*x'''[t]+8*x''[t]-8*x'[t]+4*x[t]==Sin[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \left (\frac {4}{25}+e^t (c_4 t+c_3)\right ) \cos (t)+\left (-\frac {3}{25}+e^t (c_2 t+c_1)\right ) \sin (t) \]