72.7.12 problem 12

Internal problem ID [14682]
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 : 12
Date solved : Monday, March 31, 2025 at 12:52:47 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 17

ode:=diff(y(t),t)-3*y(t)/t = 2*t^3*exp(2*t); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \left ({\mathrm e}^{2 t}-{\mathrm e}^{2}\right ) t^{3} \]

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 20

ode=D[y[t],t]-3/t*y[t]==2*t^3*Exp[2*t]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \left (e^{2 t}-e^2\right ) t^3 \]

✓ Sympy. Time used: 0.249 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*t**3*exp(2*t) + Derivative(y(t), t) - 3*y(t)/t,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = t^{3} \left (e^{2 t} - e^{2}\right ) \]