(x^2-a^2)dy=0

Solution for (x^2-a^2)dy=0 equation:

Simplifying
(x2 + -1a2) * dy = 0

Reorder the terms:
(-1a2 + x2) * dy = 0

Reorder the terms for easier multiplication:
dy(-1a2 + x2) = 0
(-1a2 * dy + x2 * dy) = 0
(-1a2dy + dx2y) = 0

Solving
-1a2dy + dx2y = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1dx2y' to each side of the equation.
-1a2dy + dx2y + -1dx2y = 0 + -1dx2y

Combine like terms: dx2y + -1dx2y = 0
-1a2dy + 0 = 0 + -1dx2y
-1a2dy = 0 + -1dx2y
Remove the zero:
-1a2dy = -1dx2y

Divide each side by '-1dy'.
a2 = x2

Simplifying
a2 = x2

Take the square root of each side:
a = {-1x, x}