23.3.437 problem 442

Internal problem ID [6151]
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 : 442
Date solved : Friday, October 03, 2025 at 01:48:01 AM
CAS classification : [_Jacobi]

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 35

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

\[ y = c_1 \operatorname {MathieuC}\left (2 a +b , -\frac {b}{2}, \arccos \left (\sqrt {x}\right )\right )+c_2 \operatorname {MathieuS}\left (2 a +b , -\frac {b}{2}, \arccos \left (\sqrt {x}\right )\right ) \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to c_1 \text {MathieuC}\left [2 a+b,-\frac {b}{2},\arccos \left (\sqrt {x}\right )\right ]+c_2 \text {MathieuS}\left [2 a+b,-\frac {b}{2},\arccos \left (\sqrt {x}\right )\right ] \end{align*}

✗ Sympy

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

False