74.7.2 problem 2

Internal problem ID [16079]
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
Date solved : Tuesday, January 28, 2025 at 08:36:53 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

\[ y = \frac {1}{1+c_{1} {\mathrm e}^{t}+t} \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 39

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

\begin{align*} y(t)\to \frac {e^{-t}}{-\int _1^te^{-K[1]} K[1]dK[1]+c_1} \\ y(t)\to 0 \\ \end{align*}