72.4.6 problem 13

Internal problem ID [14683]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.5 page 71
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 07:11:13 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 14

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

\[ y(t)\to \frac {1}{\sqrt {1-2 t}} \]