74.18.49 problem 54 (c)

Internal problem ID [16535]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 54 (c)
Date solved : Monday, March 31, 2025 at 02:55:48 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = t \left (c_1 \,t^{4}+c_2 \right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 16

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

\[ y(t)\to t \left (c_2 t^4+c_1\right ) \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = t \left (C_{1} + C_{2} t^{4}\right ) \]