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 : Monday, January 27, 2025 at 01:23:32 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

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

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

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