83.27.19 problem 19

Internal problem ID [19294]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 19
Date solved : Monday, March 31, 2025 at 07:05:53 PM
CAS classification : [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{2}+\left (2 x y-1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \end{align*}

✗ Maple

ode:=y(x)^2+(2*x*y(x)-1)*diff(y(x),x)+x*diff(diff(y(x),x),x)+x^2*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]^2+(2*x*y[x]-1)*D[y[x],x]+x*D[y[x],{x,2}]+x^2*D[y[x],{x,3}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*Derivative(y(x), (x, 3)) - x*Derivative(y(x), (x, 2)) - y(x)**2)/(2*x*y(x) - 1) cannot be solved by the factorable group method