14.2.3 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 : Monday, January 27, 2025 at 05:54:14 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 17

DSolve[D[y[t],t]==1-t+y[t]^2-t*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

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