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 : Sunday, March 30, 2025 at 12:15:47 AM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+diff(diff(y(t),t),t) = t^2; 
dsolve(ode,y(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.098 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2 + Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} t + C_{3} \sin {\left (t \right )} + C_{4} \cos {\left (t \right )} + \frac {t^{4}}{12} - t^{2} \]