72.7.6 problem 6

Internal problem ID [14668]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 6
Date solved : Thursday, March 13, 2025 at 04:13:21 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(y(t),t)-2*y(t)/t = t^3*exp(t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 19

ode=D[y[t],t]-2/t*y[t]==t^3*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to t^2 \left (e^t (t-1)+c_1\right ) \]

✓ Sympy. Time used: 0.255 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**3*exp(t) + Derivative(y(t), t) - 2*y(t)/t,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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