74.7.2 problem 2

Internal problem ID [16000]
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 : Thursday, March 13, 2025 at 07:10:19 AM
CAS classification : [_Bernoulli]

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

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

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

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

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 39

ode=D[y[t],t]+y[t]==t*y[t]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.219 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*y(t)**2 + y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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