Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Vertices $(\pm 2,0)$, foci $(\pm 3,0)$

Here, the vertices are on the x-axis.

Therefore, the equation of the hyperbola is of the form $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$.

Since the vertices are $(\pm 2,0), a=2$.

Since the foci are $(\pm 3,0), c=3$.

We know that $a^{2}+b^{2}=c^{2}$.

$\therefore 2^{2}+b^{2}=3^{2}$

$b^{2}=9-4=5$

Thus, the equation of the hyperbola is $\frac{x^{2}}{4}-\frac{y^{2}}{5}=1$.