8.2.3 problem 3

Internal problem ID [2491]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 05:36:58 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.412 (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)
 

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