11.2.4 problem 1.1-3 (d)

Internal problem ID [3428]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (d)
Date solved : Tuesday, September 30, 2025 at 06:38:05 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 21

ode:=diff(y(t),t) = t*exp(2*t); 
ic:=[y(1) = 5]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {\left (2 t -1\right ) {\mathrm e}^{2 t}}{4}+5-\frac {{\mathrm e}^{2}}{4} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 27

ode=D[y[t],t]==t*Exp[2*t]; 
ic=y[1]==5; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{4} \left (e^{2 t} (2 t-1)-e^2+20\right ) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*exp(2*t) + Derivative(y(t), t),0) 
ics = {y(1): 5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t e^{2 t}}{2} - \frac {e^{2 t}}{4} - \frac {e^{2}}{4} + 5 \]