17.2.2 problem 1.1-3 (b)

Internal problem ID [3426]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (b)
Date solved : Monday, January 27, 2025 at 07:36:19 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 13

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

\[ y = \frac {3}{\sqrt {18 t -17}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

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

\[ y(t)\to \frac {3}{\sqrt {18 t-17}} \]