8.6.13 problem 13

Internal problem ID [783]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 13
Date solved : Thursday, March 13, 2025 at 03:52:46 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \end{align*}

✗ Maple

ode:=diff(y(x),x) = 1+x^2+y(x)^2+x^2*y(x)^4; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x] == 1+x^2+y[x]^2+x^2*y[x]^4; 
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*y(x)**4 - x**2 - y(x)**2 + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x**2*y(x)**4 - x**2 - y(x)**2 + Derivative(y(x), x) - 1 cannot be solved by the lie group method