32.6.13 problem Exercise 12.13, page 103

Internal problem ID [5878]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.13, page 103
Date solved : Sunday, March 30, 2025 at 10:22:32 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 21

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

\[ x -\frac {3 \left (x^{2}+2 y-1\right )^{{1}/{3}}}{2}-c_1 = 0 \]

✓ Mathematica. Time used: 0.227 (sec). Leaf size: 40

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

\[ y(x)\to \frac {1}{54} \left (8 x^3-3 (9+8 c_1) x^2+24 c_1{}^2 x+27-8 c_1{}^3\right ) \]

✓ Sympy. Time used: 0.848 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = - \frac {x^{2}}{2} + \frac {4 \left (C_{1} + x\right )^{3}}{27} + \frac {1}{2} \]