10.3.10 problem 14

Internal problem ID [1175]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 14
Date solved : Saturday, March 29, 2025 at 10:44:34 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = \frac {1}{-t^{2}+c_1} \]

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 20

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

\begin{align*} y(t)\to -\frac {1}{t^2+c_1} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 10

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

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