90.5.20 problem 21

Internal problem ID [25139]
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 : 21
Date solved : Thursday, October 02, 2025 at 11:53:47 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {1}{\left (t +y\right )^{2}} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 19

ode:=diff(y(t),t) = 1/(y(t)+t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \operatorname {RootOf}\left (-\textit {\_Z} +c_1 -t +\tan \left (\textit {\_Z} \right )\right )-c_1 \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 16

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

\[ \text {Solve}[y(t)-\arctan (y(t)+t)=c_1,y(t)] \]

✓ Sympy. Time used: 0.460 (sec). Leaf size: 12

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

\[ C_{1} - y{\left (t \right )} + \operatorname {atan}{\left (t + y{\left (t \right )} \right )} = 0 \]