7.9.15 problem 20

Internal problem ID [2401]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 05:35:23 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

\[ y = t \left (\ln \left (t \right ) c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 15

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

\begin{align*} y(t)&\to t (c_2 \log (t)+c_1) \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 10

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

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