66.2.14 problem Problem 14

Internal problem ID [13913]
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
Date solved : Tuesday, January 28, 2025 at 06:08:23 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x&=t^{2}-3 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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: 0.003 (sec). Leaf size: 38

DSolve[D[x[t],{t,4}]-2*D[x[t],{t,2}]+x[t]==t^2-3,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t^2+c_2 e^{-t} t+c_1 e^{-t}+e^t (c_4 t+c_3)+1 \]