90.5.3 problem 3

Internal problem ID [25122]
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 : 3
Date solved : Thursday, October 02, 2025 at 11:50:50 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*}

With initial conditions

\begin{align*} y \left (2\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 7

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

\[ y = 2 t \]

✓ Mathematica. Time used: 0.278 (sec). Leaf size: 8

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

\begin{align*} y(t)&\to 2 t \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 5

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 = {y(2): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 t \]