11.1.2 problem 1.1-2 (b)

Internal problem ID [3419]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-2, page 6
Problem number : 1.1-2 (b)
Date solved : Tuesday, September 30, 2025 at 06:37:56 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {\left (2 t -1\right ) {\mathrm e}^{2 t}}{4}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to \frac {1}{4} e^{2 t} (2 t-1)+c_1 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 19

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

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