83.49.7 problem Ex 7 page 124

Internal problem ID [19541]
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 7 page 124
Date solved : Thursday, March 13, 2025 at 02:48:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y&=x \cos \left (x \right ) \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+(1+2/x*cot(x)-2/x^2)*y(x) = x*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+(1+2/x*Cot[x]-2/x^2)*y[x]==x*Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve -x*cos(x) + (1 + 2/(x*tan(x)) - 2/x**2)*y(x) + Derivative(y(x), (x, 2))