76.2.2 problem 2

Internal problem ID [17267]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 2
Date solved : Monday, March 31, 2025 at 03:48:03 PM
CAS classification : [[_linear, `class A`]]

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

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

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

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

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.172 (sec). Leaf size: 14

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

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