76.12.9 problem 15

Internal problem ID [17494]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 15
Date solved : Monday, March 31, 2025 at 04:15:46 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 18

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

\[ y(t)\to \frac {c_2 t^3+c_1}{t} \]

✓ Sympy. Time used: 0.057 (sec). Leaf size: 10

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

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