4.1.13 problem 13

Internal problem ID [1110]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 04:22:04 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to e^t \left (2 e^t (t-1)+3\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 15

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

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