77.5.17 problem 17

Internal problem ID [20397]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 17
Date solved : Thursday, October 02, 2025 at 05:52:24 PM
CAS classification : [`x=_G(y,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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