83.49.7 problem Ex 7 page 124

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 7 page 124
Date solved : Monday, March 31, 2025 at 07:33:03 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. Time used: 0.106 (sec). Leaf size: 62

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);
 

\[ y = \frac {12 \left (c_1 -\frac {1}{4}\right ) \sin \left (x \right ) x \ln \left (1-{\mathrm e}^{2 i x}\right )-6 i \left (c_1 -\frac {1}{4}\right ) \sin \left (x \right ) \operatorname {polylog}\left (2, {\mathrm e}^{2 i x}\right )-6 \left (c_1 -\frac {1}{4}\right ) x^{2} {\mathrm e}^{i x}+\sin \left (x \right ) \left (x^{3}+6 c_2 \right )}{6 x} \]

✗ 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))