39.1.6 problem Problem 11.6

Internal problem ID [6511]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.6
Date solved : Wednesday, March 05, 2025 at 12:55:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=50 t^{3}-36 t^{2}-63 t +18 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+25*y(t) = 50*t^3-36*t^2-63*t+18; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{3 t} \sin \left (4 t \right ) c_2 +{\mathrm e}^{3 t} \cos \left (4 t \right ) c_1 +2 t^{3}-3 t \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 38

ode=D[y[t],{t,2}]-6*D[y[t],t]+25*y[t]==50*t^3-36*t^2-63*t+18; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 2 t^3-3 t+c_2 e^{3 t} \cos (4 t)+c_1 e^{3 t} \sin (4 t) \]

✓ Sympy. Time used: 0.211 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-50*t**3 + 36*t**2 + 63*t + 25*y(t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 18,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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