90.4.21 problem 22

Internal problem ID [25116]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 22
Date solved : Thursday, October 02, 2025 at 11:50:37 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.097 (sec). Leaf size: 15

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

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