90.1.7 problem 18

Internal problem ID [25031]
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 13
Problem number : 18
Date solved : Thursday, October 02, 2025 at 11:47:36 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {y^{2}-4 y t +6 t^{2}}{t^{2}} \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 22

ode:=diff(y(t),t) = (y(t)^2-4*t*y(t)+6*t^2)/t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {2 c_1 \,t^{2}-3 t}{t c_1 -1} \]

✓ Mathematica. Time used: 0.309 (sec). Leaf size: 40

ode=D[y[t],{t,1}]== (y[t]^2-4*y[t]*t+6*t^2)/t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.149 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (6*t**2 - 4*t*y(t) + y(t)**2)/t**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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