68.12.28 problem 28

Internal problem ID [17622]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 28
Date solved : Thursday, October 02, 2025 at 02:26:22 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 t} \ln \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(diff(y(t),t),t)-10*diff(y(t),t)+25*y(t) = exp(5*t)*ln(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{5 t} \left (c_2 +t c_1 +\frac {t^{2} \left (2 \ln \left (2\right )+2 \ln \left (t \right )-3\right )}{4}\right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 38

ode=D[y[t],{t,2}]-10*D[y[t],t]+25*y[t]==Exp[5*t]*Log[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{4} e^{5 t} \left (-3 t^2+2 t^2 \log (2 t)+4 c_2 t+4 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.215 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) - exp(5*t)*log(2*t) - 10*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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