90.4.20 problem 21

Internal problem ID [25115]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 21
Date solved : Thursday, October 02, 2025 at 11:50:36 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(t),t)-n/t*y(t) = exp(t)*t^n; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left ({\mathrm e}^{t}+c_1 \right ) t^{n} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 15

ode=D[y[t],{t,1}] -n/t*y[t]== Exp[t] * t^n; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \left (e^t+c_1\right ) t^n \end{align*}

✓ Sympy. Time used: 3.665 (sec). Leaf size: 82

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

\[ \left [ y{\left (t \right )} = \begin {cases} \frac {C_{1} t e^{n \log {\left (t \right )}}}{n t e^{n \log {\left (t \right )}} \log {\left (t \right )} + 2 t} + \frac {t^{n + 1} e^{t}}{n t e^{n \log {\left (t \right )}} \log {\left (t \right )} + 2 t} & \text {for}\: n = 0 \vee n \geq \infty \vee n \leq -\infty \\\text {NaN} & \text {otherwise} \end {cases}, \ y{\left (t \right )} = \begin {cases} C_{1} e^{n \log {\left (t \right )}} + t^{n} e^{t} & \text {for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\text {NaN} & \text {otherwise} \end {cases}\right ] \]