68.5.29 problem 29

Internal problem ID [17280]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 29
Date solved : Thursday, October 02, 2025 at 02:00:46 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 14

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

\[ y = 1-2 \,{\mathrm e}^{-t^{2}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.162 (sec). Leaf size: 10

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

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