72.8.20 problem 33

Internal problem ID [14784]
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. Review Exercises for chapter 1. page 136
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 07:15:17 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.178 (sec). Leaf size: 18

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

\[ y = -\frac {3}{\sqrt {-6 t^{3}-18 t +36}} \]

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 28

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

\[ y(t)\to -\frac {\sqrt {\frac {3}{2}}}{\sqrt {-t^3-3 t+6}} \]