90.5.13 problem 13

Internal problem ID [25132]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 13
Date solved : Thursday, October 02, 2025 at 11:53:30 PM
CAS classification : [_separable]

\begin{align*} \left (-t^{2}+1\right ) y^{\prime }-y t&=5 t y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=(-t^2+1)*diff(y(t),t)-t*y(t) = 5*t*y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {1}{-5+\sqrt {t -1}\, \sqrt {t +1}\, c_1} \]

✓ Mathematica. Time used: 1.878 (sec). Leaf size: 42

ode=(1-t^2)*D[y[t],{t,1}] -t*y[t] == 5*t*y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {e^{c_1}}{\sqrt {1-t^2}-5 e^{c_1}}\\ y(t)&\to -\frac {1}{5}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.968 (sec). Leaf size: 48

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-5*t*y(t)**2 - t*y(t) + (1 - t**2)*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \frac {- C_{1} + \sqrt {C_{1} \left (t^{2} - 1\right )}}{5 \left (C_{1} - t^{2} + 1\right )}, \ y{\left (t \right )} = \frac {C_{1} + \sqrt {C_{1} \left (t^{2} - 1\right )}}{5 \left (- C_{1} + t^{2} - 1\right )}\right ] \]