72.1.2 problem 5

Internal problem ID [14523]
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 : Thursday, March 13, 2025 at 03:32:13 AM
CAS classification : [_separable]

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

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

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

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

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

ode=D[y[t],t]==(t*y[t])^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.151 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2*y(t)**2 + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {3}{C_{1} + t^{3}} \]