74.18.44 problem 50

Internal problem ID [16522]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 50
Date solved : Thursday, March 13, 2025 at 08:16:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

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

\[ y = \frac {{\mathrm e}^{t} \left (2 \ln \left (t \right ) t^{2}+4 c_{1} t -3 t^{2}+4 c_{2} \right )}{4} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 0.266 (sec). Leaf size: 22

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

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