76.12.5 problem 5

Internal problem ID [17482]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 5
Date solved : Thursday, March 13, 2025 at 10:10:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x +3\right ) y^{\prime \prime }+x y^{\prime }+\ln \left (x \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1 \end{align*}

✗ Maple

ode:=(x+3)*diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x)*ln(x) = 0; 
ic:=y(1) = 0, D(y)(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x+3)*D[y[x],{x,2}]+x*D[y[x],x]+Log[x]*y[x]==0; 
ic={y[1]==0,Derivative[1][y][1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (x + 3)*Derivative(y(x), (x, 2)) + y(x)*log(x),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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