15.1.28 problem 28

Internal problem ID [2868]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 28
Date solved : Sunday, March 30, 2025 at 12:35:16 AM
CAS classification : [_rational, _Abel]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.133 (sec). Leaf size: 7

ode:=x^2+3*x*diff(y(x),x) = y(x)^3+2*y(x); 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = x^{{2}/{3}} \]

✗ Mathematica

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

{}

✗ Sympy

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

IndexError : Index out of range: a[1]