90.3.3 problem 3

Internal problem ID [25067]
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 41
Problem number : 3
Date solved : Thursday, October 02, 2025 at 11:48:12 PM
CAS classification : [_linear]

\begin{align*} t^{2} y^{\prime }&=1-2 y t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \frac {t +c_1}{t^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 13

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

\begin{align*} y(t)&\to \frac {t+c_1}{t^2} \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 8

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

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