23.3.321 problem 323

Internal problem ID [6035]
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 : 323
Date solved : Tuesday, September 30, 2025 at 02:20:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\[ y = {\mathrm e}^{-x} c_2 +{\mathrm e}^{2 x} c_1 -\ln \left (x \right ) \]

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to -\log (x)+c_1 e^{-x}+c_2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.248 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{2 x} - \log {\left (x \right )} \]