23.3.284 problem 286

Internal problem ID [5998]
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 : 286
Date solved : Tuesday, September 30, 2025 at 02:07:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 19

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

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