14.11.17 problem 18 (b)

Internal problem ID [2610]
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 : 18 (b)
Date solved : Sunday, March 30, 2025 at 12:11:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t^{{3}/{2}} {\mathrm e}^{3 t} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+9*y(t) = t^(3/2)*exp(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{3 t} \left (c_2 +t c_1 +\frac {4 t^{{7}/{2}}}{35}\right ) \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 31

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

\[ y(t)\to \frac {1}{35} e^{3 t} \left (4 t^{7/2}+35 c_2 t+35 c_1\right ) \]

✓ Sympy. Time used: 0.262 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**(3/2)*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)
 

\[ y{\left (t \right )} = \left (C_{1} + t \left (C_{2} + \frac {4 t^{\frac {5}{2}}}{35}\right )\right ) e^{3 t} \]