90.5.11 problem 11

Internal problem ID [25130]
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 71
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:53:24 PM
CAS classification : [_separable]

\begin{align*} y t +y^{\prime }&=t y^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(y(t),t)+t*y(t) = t*y(t)^3; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{t^{2}} c_1 +1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{t^{2}} c_1 +1}} \\ \end{align*}

✓ Mathematica. Time used: 1.763 (sec). Leaf size: 58

ode=D[y[t],{t,1}] +t*y[t] == t*y[t]^3; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {1}{\sqrt {1+e^{t^2+2 c_1}}}\\ y(t)&\to \frac {1}{\sqrt {1+e^{t^2+2 c_1}}}\\ y(t)&\to -1\\ y(t)&\to 0\\ y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.835 (sec). Leaf size: 34

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*y(t)**3 + t*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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