Internal problem ID [4026]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }-\left (x^{2}+2 y-1\right )^{\frac {2}{3}}+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve(diff(y(x),x)=(x^2+2*y(x)-1)^(2/3)-x,y(x), singsol=all)
\[ x -\frac {3 \left (x^{2}+2 y \relax (x )-1\right )^{\frac {1}{3}}}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.359 (sec). Leaf size: 40
DSolve[y'[x]==(x^2+2*y[x]-1)^(2/3)-x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}