8.7.30 problem 55

Internal problem ID [836]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 55
Date solved : Tuesday, March 04, 2025 at 11:53:10 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 13

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

\[ y(x)\to c_1 \log (x)+c_2 \]

✓ Sympy. Time used: 0.129 (sec). Leaf size: 8

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

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