75.20.25 problem 664

Internal problem ID [17088]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 664
Date solved : Monday, March 31, 2025 at 03:40:25 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 29

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

\[ y(x)\to x \log ^2(x)-(-2+c_1) x+(-2+c_1) x \log (x)+c_2 \]

✗ Sympy

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

NotImplementedError : The given ODE -(x*Derivative(y(x), (x, 2)) - log(x))*log(x) + Derivative(y(x), x) cannot be solved by the factorable group method