23.3.385 problem 389

Internal problem ID [6099]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 389
Date solved : Tuesday, September 30, 2025 at 02:21:32 PM
CAS classification : [_Jacobi]

\begin{align*} 6 y+2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 54

ode:=6*y(x)+2*diff(y(x),x)+(1-x)*x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (-1+x \right )^{3}+\frac {12 \left (-x \left (-1+x \right )^{3} \ln \left (-1+x \right )+x \left (-1+x \right )^{3} \ln \left (x \right )-x^{3}+\frac {5 x^{2}}{2}-\frac {11 x}{6}+\frac {1}{4}\right ) c_2}{x} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 90

ode=6*y[x] + 2*D[y[x],x] + (1 - x)*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-3 c_1 x^4+9 c_1 x^3+12 c_2 x^3-9 c_1 x^2-30 c_2 x^2+3 c_1 x+22 c_2 x+12 c_2 (x-1)^3 x \log (1-x)-12 c_2 (x-1)^3 x \log (x)-3 c_2}{3 x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x)*Derivative(y(x), (x, 2)) + 6*y(x) + 2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x**2*Derivative(y(x), (x, 2))/2 + x*Derivative(y(x), (x, 2))/2