10.9.27 problem 42

Internal problem ID [1329]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 42
Date solved : Tuesday, March 04, 2025 at 12:29:15 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = c_1 t +c_2 \,t^{{5}/{2}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

ode=2*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]
 

\[ y(t)\to t \left (c_2 t^{3/2}+c_1\right ) \]

✓ Sympy. Time used: 0.153 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*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)
 

\[ y{\left (t \right )} = C_{1} t + C_{2} t^{\frac {5}{2}} \]