90.22.4 problem 4

Internal problem ID [25342]
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 : 4
Date solved : Friday, October 03, 2025 at 12:00:24 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.100 (sec). Leaf size: 19

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

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