Internal problem ID [12197]
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 49.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime \prime \prime }+x=t^{3}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 67
dsolve(diff(x(t),t$4)+x(t)=t^3,x(t), singsol=all)
\[ x \left (t \right ) = \left (c_{2} {\mathrm e}^{-\frac {\sqrt {2}\, t}{2}}+c_{4} {\mathrm e}^{\frac {\sqrt {2}\, t}{2}}\right ) \sin \left (\frac {\sqrt {2}\, t}{2}\right )+t^{3}+c_{1} {\mathrm e}^{-\frac {\sqrt {2}\, t}{2}} \cos \left (\frac {\sqrt {2}\, t}{2}\right )+c_{3} {\mathrm e}^{\frac {\sqrt {2}\, t}{2}} \cos \left (\frac {\sqrt {2}\, t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 78
DSolve[x''''[t]+x[t]==t^3,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-\frac {t}{\sqrt {2}}} \left (e^{\frac {t}{\sqrt {2}}} t^3+\left (c_1 e^{\sqrt {2} t}+c_2\right ) \cos \left (\frac {t}{\sqrt {2}}\right )+\left (c_4 e^{\sqrt {2} t}+c_3\right ) \sin \left (\frac {t}{\sqrt {2}}\right )\right ) \]