90.20.15 problem 16 (2)

Internal problem ID [25310]
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 : 16 (2)
Date solved : Thursday, October 02, 2025 at 11:59:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=(t^2+1)*diff(diff(y(t),t),t)-4*t*diff(y(t),t)+6*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_2 \,t^{3}-3 c_1 \,t^{2}-3 c_2 t +c_1 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 33

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

\begin{align*} y(t)&\to -\frac {1}{3} i \left (c_2 \left (3 t^2-1\right )+3 c_1 (t-i)^3\right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*t*Derivative(y(t), t) + (t**2 + 1)*Derivative(y(t), (t, 2)) + 6*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

False