23.3.428 problem 433

Internal problem ID [6142]
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 : 433
Date solved : Tuesday, September 30, 2025 at 02:22:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.048 (sec). Leaf size: 61

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

\[ y = x^{2} {\mathrm e}^{-2 x} c_2 -\frac {16 c_1 \left (-x^{{5}/{2}} \sqrt {2}\, \sqrt {\pi }\, \operatorname {erfi}\left (\sqrt {2}\, \sqrt {x}\right ) {\mathrm e}^{-2 x}+x^{2}+\frac {x}{4}+\frac {3}{16}\right )}{\sqrt {x}}+\frac {x^{3}}{18}+\frac {11 x^{2}}{252} \]

✓ Mathematica. Time used: 0.68 (sec). Leaf size: 83

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

\begin{align*} y(x)&\to \frac {1}{252} (14 x+11) x^2+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(-x**3*(x + 1) + 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)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x**4 + x**3 - 2*x**2*Derivative(y(x), (x,