23.3.389 problem 393

Internal problem ID [6103]
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 : 393
Date solved : Tuesday, September 30, 2025 at 02:21:35 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 45

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

\[ y = \frac {-6 x^{6}+20 c_2 \,x^{4}+12 x^{5}+10 x^{3}+80 c_1 x -5 x^{2}-60 c_1}{20 \left (x -1\right )^{2}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 51

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

\begin{align*} y(x)&\to \frac {-18 x^6+36 x^5+60 c_1 x^4+30 x^3-15 x^2+20 c_2 x-15 c_2}{60 (x-1)^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x)*Derivative(y(x), (x, 2)) - x*(3*x**3 + 1) + 2*y(x) - 3*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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