Internal problem ID [14345]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }+y-t y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(t),t)+y(t)=t*y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{1+{\mathrm e}^{t} c_{1} +t} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 21
DSolve[y'[t]+y[t]==t*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{t+c_1 e^t+1} \\ y(t)\to 0 \\ \end{align*}