90.5.17 problem 17

Internal problem ID [25136]
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 : 17
Date solved : Thursday, October 02, 2025 at 11:53:42 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 t} c_1 +4 t}} \\ y &= \frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 t} c_1 +4 t}} \\ \end{align*}

✓ Mathematica. Time used: 2.398 (sec). Leaf size: 50

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

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

✓ Sympy. Time used: 0.460 (sec). Leaf size: 49

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

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