Internal problem ID [11727]
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 (iv).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x={\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(x(t),t$4)-5*diff(x(t),t$2)+4*x(t)=exp(t),x(t), singsol=all)
\[ x \left (t \right ) = -\frac {t \,{\mathrm e}^{t}}{6}+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-2 t}+c_{3} {\mathrm e}^{-t}+{\mathrm e}^{2 t} c_{4} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 45
DSolve[x''''[t]-5*x''[t]+4*x[t]==Exp[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-2 t} \left (c_2 e^t+e^{3 t} \left (-\frac {t}{6}-\frac {1}{36}+c_3\right )+c_4 e^{4 t}+c_1\right ) \]