83.48.8 problem Ex 8 page 103

Internal problem ID [19521]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 8 page 103
Date solved : Thursday, March 13, 2025 at 02:44:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y+3 x y^{\prime }+2 y {y^{\prime }}^{2}+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=y(x)+3*x*diff(y(x),x)+2*y(x)*diff(y(x),x)^2+(x^2+2*y(x)^2*diff(y(x),x))*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -(-3*x + sqrt(-8*x**2*y(x)*Derivative(y(x), (x, 2)) + 9*x**2 + 12*x*y(x)**2*Derivative(y(x), (x, 2)) + 4*y(x)**4*Derivative(y(x), (x, 2))**2 - 8*y(x)**2) - 2*y(x)**2*Derivative(y(x), (x, 2)))/(4*y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method