90.6.7 problem 7

Internal problem ID [25151]
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 : 7
Date solved : Thursday, October 02, 2025 at 11:55:04 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 y t +2 t^{3}+\left (t^{2}-y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 35

ode:=2*t*y(t)+2*t^3+(t^2-y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= t^{2}-\sqrt {2 t^{4}+c_1} \\ y &= t^{2}+\sqrt {2 t^{4}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 53

ode=2*t*y[t]+2*t^3+(t^2-y[t])*D[y[t],t]== 0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t^2-i \sqrt {-2 t^4-c_1}\\ y(t)&\to t^2+i \sqrt {-2 t^4-c_1} \end{align*}

✓ Sympy. Time used: 0.624 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t**3 + 2*t*y(t) + (t**2 - y(t))*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = t^{2} - \sqrt {C_{1} + 2 t^{4}}, \ y{\left (t \right )} = t^{2} + \sqrt {C_{1} + 2 t^{4}}\right ] \]