69.20.29 problem 668

Internal problem ID [18450]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 668
Date solved : Friday, October 03, 2025 at 07:32:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 x y^{\prime \prime }+2 y^{\prime }+y&=\frac {6+x}{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.756 (sec). Leaf size: 5

ode:=4*x*diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = (x+6)/x^2; 
ic:=[y(infinity) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \textit {undefined} \]

✗ Mathematica

ode=4*x*D[y[x],{x,2}]+2*D[y[x],x]+y[x]==(6+x)/x^2; 
ic={y[Infinity]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), (x, 2)) + y(x) + 2*Derivative(y(x), x) - (x + 6)/x**2,0) 
ics = {y(oo): 0} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*(4*x*Derivative(y(x), (x, 2)) + y(x)) + x + 6)/(2*x**2) cannot be solved by the factorable group method