90.3.6 problem 6

Internal problem ID [25070]
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 41
Problem number : 6
Date solved : Thursday, October 02, 2025 at 11:48:15 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \tan \left (\frac {1}{2} t^{2}+c_1 -t \right ) \]

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 21

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

\begin{align*} y(t)&\to \tan \left (\frac {1}{2} \left (t^2-2 t+2 c_1\right )\right ) \end{align*}

✓ Sympy. Time used: 0.379 (sec). Leaf size: 12

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

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