Internal problem ID [12177]
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 14.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x=t^{2}-3} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(x(t),t$4)-2*diff(x(t),t$2)+x(t)=t^2-3,x(t), singsol=all)
\[ x \left (t \right ) = \left (c_{4} t +c_{2} \right ) {\mathrm e}^{-t}+\left (c_{3} t +c_{1} \right ) {\mathrm e}^{t}+t^{2}+1 \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 38
DSolve[x''''[t]-2*x''[t]+x[t]==t^2-3,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to t^2+c_2 e^{-t} t+c_1 e^{-t}+e^t (c_4 t+c_3)+1 \]