72.1.25 problem 28

Internal problem ID [14625]
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 1.2. page 33
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 06:44:57 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=t^{2} y^{3} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.161 (sec). Leaf size: 15

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

\[ y = -\frac {3}{\sqrt {-6 t^{3}+9}} \]

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 20

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

\[ y(t)\to -\frac {1}{\sqrt {1-\frac {2 t^3}{3}}} \]