12.4.15 problem 18

Internal problem ID [1622]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 18
Date solved : Saturday, March 29, 2025 at 11:08:05 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x \left (y-1\right )^{{1}/{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 5

ode:=diff(y(x),x) = 3*x*(y(x)-1)^(1/3); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 1 \]

✓ Mathematica. Time used: 0.265 (sec). Leaf size: 19

ode=D[y[x],x]==3*x*(y[x]-1)^(1/3); 
ic=y[0]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to 1 \\ y(x)\to \left (x^2\right )^{3/2}+1 \\ \end{align*}

✓ Sympy. Time used: 1.282 (sec). Leaf size: 27

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

\[ \left [ y{\left (x \right )} = - x^{2} \sqrt {x^{2}} + 1, \ y{\left (x \right )} = x^{2} \sqrt {x^{2}} + 1\right ] \]