66.1.23 problem Problem 31

Internal problem ID [13791]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 31
Date solved : Wednesday, March 05, 2025 at 10:16:55 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }&=x y^{3}+x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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