74.3.33 problem 28

Internal problem ID [15893]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 08:17:40 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 11

dsolve([diff(y(t),t)=-y(t)^3,y(0) = 1/2],y(t), singsol=all)
 

\[ y = \frac {1}{\sqrt {4+2 t}} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

DSolve[{D[y[t],t]==-y[t]^3,{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {i}{\sqrt {-2 t-4}} \]