90.6.8 problem 8

Internal problem ID [25152]
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 : 8
Date solved : Thursday, October 02, 2025 at 11:55:07 PM
CAS classification : [_linear]

\begin{align*} t^{2}-y-t y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \frac {t^{3}+3 c_1}{3 t} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to \frac {t^2}{3}+\frac {c_1}{t} \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 10

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

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