Internal problem ID [932]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } y x^{2}-\left (-1+y^{2}\right )^{\frac {3}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^2*y(x)*diff(y(x),x)= (y(x)^2-1)^(3/2),y(x), singsol=all)
\[ -\frac {1}{x}+\frac {\left (y \relax (x )-1\right ) \left (y \relax (x )+1\right )}{\left (y \relax (x )^{2}-1\right )^{\frac {3}{2}}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.726 (sec). Leaf size: 105
DSolve[x^2*y[x]*y'[x]== (y[x]^2-1)^(3/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {1+x \left (x+c_1{}^2 x-2 c_1\right )}}{1-c_1 x} \\ y(x)\to \frac {\sqrt {1+x \left (x+c_1{}^2 x-2 c_1\right )}}{-1+c_1 x} \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to -\frac {x}{\sqrt {x^2}} \\ y(x)\to \frac {x}{\sqrt {x^2}} \\ \end{align*}