90.6.2 problem 2

Internal problem ID [25146]
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 83
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:54:44 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y-t +\left (t +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 53

ode:=y(t)-t+(t+2*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {-t c_1 -\sqrt {3 t^{2} c_1^{2}+2}}{2 c_1} \\ y &= \frac {-t c_1 +\sqrt {3 t^{2} c_1^{2}+2}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.265 (sec). Leaf size: 114

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

\begin{align*} y(t)&\to \frac {1}{2} \left (-t-\sqrt {3 t^2+2 e^{2 c_1}}\right )\\ y(t)&\to \frac {1}{2} \left (-t+\sqrt {3 t^2+2 e^{2 c_1}}\right )\\ y(t)&\to \frac {1}{2} \left (-\sqrt {3} \sqrt {t^2}-t\right )\\ y(t)&\to \frac {1}{2} \left (\sqrt {3} \sqrt {t^2}-t\right ) \end{align*}

✓ Sympy. Time used: 0.795 (sec). Leaf size: 36

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

\[ \left [ y{\left (t \right )} = - \frac {t}{2} - \frac {\sqrt {C_{1} + 3 t^{2}}}{2}, \ y{\left (t \right )} = - \frac {t}{2} + \frac {\sqrt {C_{1} + 3 t^{2}}}{2}\right ] \]