90.2.11 problem 11

Internal problem ID [25062]
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 23
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:48:07 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }&=y \left (t +y\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(y(t),t) = y(t)*(y(t)+t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {2 \,{\mathrm e}^{\frac {t^{2}}{2}}}{i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, t}{2}\right )+2 c_1} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 45

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

\begin{align*} y(t)&\to \frac {2 e^{\frac {t^2}{2}}}{-\sqrt {2 \pi } \text {erfi}\left (\frac {t}{\sqrt {2}}\right )+2 c_1}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 32

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

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