63.14.5 problem 1(e)

Internal problem ID [13110]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.5 Higher order equations. Exercises page 130
Problem number : 1(e)
Date solved : Monday, March 31, 2025 at 07:34:32 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=diff(diff(diff(x(t),t),t),t)+diff(diff(x(t),t),t) = 2*exp(t)+3*t^2; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {t^{4}}{4}+3 t^{2}-t^{3}+{\mathrm e}^{-t} c_1 +{\mathrm e}^{t}+c_2 t +c_3 \]

✓ Mathematica. Time used: 16.229 (sec). Leaf size: 63

ode=D[x[t],{t,3}]+D[x[t],{t,2}]==2*Exp[t]+3*t^2; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \int _1^t\int _1^{K[3]}e^{-K[2]} \left (c_1+\int _1^{K[2]}e^{K[1]} \left (3 K[1]^2+2 e^{K[1]}\right )dK[1]\right )dK[2]dK[3]+c_3 t+c_2 \]

✓ Sympy. Time used: 0.124 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-3*t**2 - 2*exp(t) + Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} + C_{2} t + C_{3} e^{- t} + \frac {t^{4}}{4} - t^{3} + 3 t^{2} + e^{t} \]