83.25.3 problem 3

Internal problem ID [19252]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (B) at page 83
Problem number : 3
Date solved : Monday, March 31, 2025 at 07:03:19 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = x \left (c_1 \sin \left (2 \ln \left (x \right )\right )+c_2 \cos \left (2 \ln \left (x \right )\right )\right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 24

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

\[ y(x)\to x (c_2 \cos (2 \log (x))+c_1 \sin (2 \log (x))) \]

✓ Sympy. Time used: 0.164 (sec). Leaf size: 20

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

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