90.4.23 problem 24

Internal problem ID [25118]
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 : 24
Date solved : Thursday, October 02, 2025 at 11:50:41 PM
CAS classification : [_linear]

\begin{align*} 2 y t +y^{\prime }&=1 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 20

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

\[ y = \frac {\left (\sqrt {\pi }\, \operatorname {erfi}\left (t \right )+2\right ) {\mathrm e}^{-t^{2}}}{2} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to \frac {1}{2} e^{-t^2} \left (\sqrt {\pi } \text {erfi}(t)+2\right ) \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = \left (\frac {\sqrt {\pi } \operatorname {erfi}{\left (t \right )}}{2} + 1\right ) e^{- t^{2}} \]