14.21.16 problem 16

Internal problem ID [2725]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
Problem number : 16
Date solved : Monday, January 27, 2025 at 06:12:22 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(t),t$4)+diff(y(t),t$2)=t^2,y(t), singsol=all)
 

\[ y = \frac {t^{4}}{12}-t^{2}-\cos \left (t \right ) c_1 -\sin \left (t \right ) c_2 +c_3 t +c_4 \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 36

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

\[ y(t)\to \frac {t^4}{12}-t^2+c_4 t-c_1 \cos (t)-c_2 \sin (t)+c_3 \]