14.5.5 problem 5

Internal problem ID [2542]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.17. What to do in practice. Excercises page 126
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:59:48 AM
CAS classification : [_Bernoulli]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 19

dsolve([diff(y(t),t)=t*y(t)^3-y(t),y(0) = 1],y(t), singsol=all)
 

\[ y = \frac {2}{\sqrt {2+4 t +2 \,{\mathrm e}^{2 t}}} \]

✓ Solution by Mathematica

Time used: 3.236 (sec). Leaf size: 25

DSolve[{D[y[t],t]==t*y[t]^3-y[t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\sqrt {2}}{\sqrt {2 t+e^{2 t}+1}} \]