90.15.8 problem 8

Internal problem ID [25255]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 251
Problem number : 8
Date solved : Thursday, October 02, 2025 at 11:59:23 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=10 t \,{\mathrm e}^{4 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(t),t),t)-5*diff(y(t),t)-6*y(t) = 10*exp(4*t)*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{6 t} c_2 +{\mathrm e}^{-t} c_1 +{\mathrm e}^{4 t} \left (-t -\frac {3}{10}\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 35

ode=D[y[t],{t,2}]-5*D[y[t],{t,1}]-6*y[t]==10*t*Exp[4*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{4 t} \left (-t-\frac {3}{10}\right )+c_1 e^{-t}+c_2 e^{6 t} \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 42

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-10*t*exp(4*t) - 6*y(t) - 4*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sin {\left (\frac {\sqrt {6} t}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {6} t}{2} \right )} - \frac {t e^{4 t}}{7} + \frac {16 e^{4 t}}{245} \]