72.1.2 problem 5

Internal problem ID [14602]
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 : 5
Date solved : Tuesday, January 28, 2025 at 06:44:10 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(t),t)=(t*y(t))^2,y(t), singsol=all)
 

\[ y = -\frac {3}{t^{3}-3 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 22

DSolve[D[y[t],t]==(t*y[t])^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\frac {3}{t^3+3 c_1} \\ y(t)\to 0 \\ \end{align*}