35.7.23 problem 28

Internal problem ID [6205]
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 : 28
Date solved : Sunday, March 30, 2025 at 10:43:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

ode:=3*x*diff(diff(y(x),x),x)-2*(3*x-1)*diff(y(x),x)+(3*x-2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_2 \,x^{{1}/{3}}+c_1 \right ) \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 21

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

\[ y(x)\to e^x \left (3 c_2 \sqrt [3]{x}+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), (x, 2)) + (3*x - 2)*y(x) - (6*x - 2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False