Internal problem ID [967]
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: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x \left (-1+y^{2}\right )^{\frac {2}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(x),x)=x*(y(x)^2-1)^(2/3),y(x), singsol=all)
\[ \frac {x^{2}}{2}-\frac {\left (-\mathrm {signum}\left (y \relax (x )^{2}-1\right )\right )^{\frac {2}{3}} y \relax (x ) \hypergeom \left (\left [\frac {1}{2}, \frac {2}{3}\right ], \left [\frac {3}{2}\right ], y \relax (x )^{2}\right )}{\mathrm {signum}\left (y \relax (x )^{2}-1\right )^{\frac {2}{3}}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 6.781 (sec). Leaf size: 66
DSolve[y'[x]==x*(y[x]^2-1)^(2/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1} \left (1-\text {$\#$1}^2\right )^{2/3} \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {3}{2};\text {$\#$1}^2\right )}{\left (\text {$\#$1}^2-1\right )^{2/3}}\&\right ]\left [\frac {x^2}{2}+c_1\right ] \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}