83.49.15 problem Ex 15 page 131

Internal problem ID [19549]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 15 page 131
Date solved : Thursday, March 13, 2025 at 02:49:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 30

ode:=x^6*diff(diff(y(x),x),x)+3*x^5*diff(y(x),x)+a^2*y(x) = 1/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \sin \left (\frac {a}{2 x^{2}}\right ) c_{2} +\cos \left (\frac {a}{2 x^{2}}\right ) c_{1} +\frac {1}{a^{2} x^{2}} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 38

ode=x^6*D[y[x],{x,2}]+3*x^5*D[y[x],x]+a^2*y[x]==1/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{a^2 x^2}+c_1 \cos \left (\frac {a}{2 x^2}\right )-c_2 \sin \left (\frac {a}{2 x^2}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a**2*y(x) + x**6*Derivative(y(x), (x, 2)) + 3*x**5*Derivative(y(x), x) - 1/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-a**2*x**2*y(x) - x**8*Derivative(y(x), (x, 2)) + 1)/(3*x**7) cannot be solved by the factorable group method