90.5.9 problem 9

Internal problem ID [25128]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:53:21 PM
CAS classification : [_Bernoulli]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 11

ode:=diff(y(t),t)-y(t) = t*y(t)^2; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {1}{t -1} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 12

ode=D[y[t],{t,1}] -y[t] == t*y[t]^2; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{1-t} \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*y(t)**2 - y(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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