74.8.24 problem 24

Internal problem ID [16081]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 24
Date solved : Thursday, March 13, 2025 at 07:48:31 AM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.006 (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 c_{1} {\mathrm e}^{-2 t}-4 t}} \\ y &= \frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{-2 t}-4 t}} \\ \end{align*}

✓ Mathematica. Time used: 0.185 (sec). Leaf size: 73

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

\begin{align*} y(t)\to -\frac {e^t}{\sqrt {-2 \int _1^te^{2 K[1]} K[1]dK[1]+c_1}} \\ y(t)\to \frac {e^t}{\sqrt {-2 \int _1^te^{2 K[1]} K[1]dK[1]+c_1}} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.787 (sec). Leaf size: 63

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)
 

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