90.5.19 problem 20

Internal problem ID [25138]
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 : 20
Date solved : Thursday, October 02, 2025 at 11:53:46 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (t -y\right )^{2} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 31

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

\[ y = \frac {\left (-t +1\right ) {\mathrm e}^{2 t}+c_1 \left (t +1\right )}{-{\mathrm e}^{2 t}+c_1} \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 29

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

\begin{align*} y(t)&\to t+\frac {1}{\frac {1}{2}+c_1 e^{2 t}}-1\\ y(t)&\to t-1 \end{align*}

✓ Sympy. Time used: 0.161 (sec). Leaf size: 26

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

\[ y{\left (t \right )} = \frac {C_{1} t + C_{1} - t e^{2 t} + e^{2 t}}{C_{1} - e^{2 t}} \]