35.7.25 problem 30

Internal problem ID [6207]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 30
Date solved : Wednesday, March 05, 2025 at 12:24:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=x -1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=x*(1+x)*diff(diff(y(x),x),x)-(x-1)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x -1\right ) c_{2} \ln \left (x \right )-4 c_{2} +c_{1} \left (x -1\right ) \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 23

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

\[ y(x)\to c_1 (x-1)+c_2 ((x-1) \log (x)-4) \]

✗ Sympy

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

False