90.22.2 problem 2

Internal problem ID [25340]
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 353
Problem number : 2
Date solved : Friday, October 03, 2025 at 12:00:23 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 2 t^{2} y^{\prime \prime }-5 t y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=2*t^2*diff(diff(y(t),t),t)-5*t*diff(y(t),t)+3*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 20

ode=2*t^2*D[y[t],{t,2}]-5*t*D[y[t],t]+3*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t**2*Derivative(y(t), (t, 2)) - 5*t*Derivative(y(t), t) + 3*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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