90.20.38 problem 25

Internal problem ID [25333]
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 337
Problem number : 25
Date solved : Friday, October 03, 2025 at 12:00:17 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 13

ode:=t^2*diff(diff(y(t),t),t)-4*t*diff(y(t),t)+6*y(t) = 0; 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = t^{2} \left (c_2 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 16

ode=t^2*D[y[t],{t,2}]-4*t*D[y[t],t]+6*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t^2 (c_2 t+c_1) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) - 4*t*Derivative(y(t), t) + 6*y(t),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

ValueError : Couldnt solve for initial conditions