72.8.24 problem 37

Internal problem ID [14717]
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 : 37
Date solved : Monday, March 31, 2025 at 12:55:11 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.053 (sec). Leaf size: 16

ode:=diff(y(t),t) = 2*t*y(t)^2+3*t^2*y(t)^2; 
ic:=y(1) = -1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {1}{t^{3}+t^{2}-1} \]

✓ Mathematica. Time used: 0.155 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.183 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*t**2*y(t)**2 - 2*t*y(t)**2 + Derivative(y(t), t),0) 
ics = {y(1): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {1}{t^{3} + t^{2} - 1} \]