90.21.4 problem 11

Internal problem ID [25338]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 347
Problem number : 11
Date solved : Friday, October 03, 2025 at 12:00:21 AM
CAS classification : [[_2nd_order, _missing_y]]

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

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

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

\[ y = c_2 \,t^{3}+c_1 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 17

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

\begin{align*} y(t)&\to \frac {c_1 t^3}{3}+c_2 \end{align*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 8

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

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