14.11.8 problem 8

Internal problem ID [2601]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
Problem number : 8
Date solved : Tuesday, March 04, 2025 at 02:29:37 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+9*y(t) = (3*t^7-5*t^4)*exp(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{3 t} \left (c_2 +c_1 t +\frac {1}{24} t^{9}-\frac {1}{6} t^{6}\right ) \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 32

ode=D[y[t],{t,2}]-6*D[y[t],t]+9*y[t]==(3*t^7-5*t^4)*Exp[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{24} e^{3 t} \left (t^9-4 t^6+24 c_2 t+24 c_1\right ) \]

✓ Sympy. Time used: 0.466 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((-3*t**7 + 5*t**4)*exp(3*t) + 9*y(t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + t \left (C_{2} + \frac {t^{8}}{24} - \frac {t^{5}}{6}\right )\right ) e^{3 t} \]