Internal problem ID [1670]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-1+t -y^{2}+t y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(diff(y(t),t) = 1-t+y(t)^2-t*y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = -\tan \left (\frac {1}{2} t^{2}+c_{1}-t \right ) \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 17
DSolve[y'[t] == 1-t+y[t]^2-t*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \tan \left (-\frac {t^2}{2}+t+c_1\right ) \\ \end{align*}