23.3.427 problem 432

Internal problem ID [6141]
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 : 432
Date solved : Tuesday, September 30, 2025 at 02:22:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -2 \left (1-3 x \right ) y-\left (1-4 x \right ) x y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 54

ode:=-2*(1-3*x)*y(x)-(1-4*x)*x*diff(y(x),x)+2*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {16 \left (-x^{{5}/{2}} \sqrt {\pi }\, \sqrt {2}\, {\mathrm e}^{-2 x} \operatorname {erfi}\left (\sqrt {2}\, \sqrt {x}\right ) c_2 -\frac {c_1 \,x^{{5}/{2}} {\mathrm e}^{-2 x}}{16}+c_2 \left (x^{2}+\frac {1}{4} x +\frac {3}{16}\right )\right )}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.184 (sec). Leaf size: 71

ode=-2*(1 - 3*x)*y[x] - (1 - 4*x)*x*D[y[x],x] + 2*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-2 x} x^2-\frac {2 c_2 e^{-2 x} \left (e^{2 x} \left (16 x^2+4 x+3\right )-16 \sqrt {2} (-x)^{5/2} \Gamma \left (\frac {1}{2},-2 x\right )\right )}{15 \sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - x*(1 - 4*x)*Derivative(y(x), x) + (6*x - 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False