67.2.48 problem Problem 19(a)

Internal problem ID [13926]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 19(a)
Date solved : Wednesday, March 05, 2025 at 10:22:34 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1&=0 \end{align*}

✗ Maple

ode:=x*diff(diff(y(x),x),x)+(6*x*y(x)^2+1)*diff(y(x),x)+2*y(x)^3+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x*D[y[x],{x,2}]+(6*x*y[x]^2+1)*D[y[x],x]+2*y[x]^3+1==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*Derivative(y(x), (x, 2)) + (6*x*y(x)**2 + 1)*Derivative(y(x), x) + 2*y(x)**3 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x*Derivative(y(x), (x, 2)) - 2*y(x)**3 - 1)/(6*x*y(x)**2 + 1) cannot be solved by the factorable group method