Simplifying

x(1 + -1x2) * dy + (2x2y + -1y + -1ax3) * dx = 0

Reorder the terms for easier multiplication:

x * dy(1 + -1x2) + (2x2y + -1y + -1ax3) * dx = 0

Multiply x * dy

dxy(1 + -1x2) + (2x2y + -1y + -1ax3) * dx = 0

(1 * dxy + -1x2 * dxy) + (2x2y + -1y + -1ax3) * dx = 0

(1dxy + -1dx3y) + (2x2y + -1y + -1ax3) * dx = 0

Reorder the terms:

1dxy + -1dx3y + (-1ax3 + 2x2y + -1y) * dx = 0

Reorder the terms for easier multiplication:

1dxy + -1dx3y + dx(-1ax3 + 2x2y + -1y) = 0

1dxy + -1dx3y + (-1ax3 * dx + 2x2y * dx + -1y * dx) = 0

Reorder the terms:

1dxy + -1dx3y + (-1adx4 + -1dxy + 2dx3y) = 0

1dxy + -1dx3y + (-1adx4 + -1dxy + 2dx3y) = 0

Reorder the terms:

-1adx4 + 1dxy + -1dxy + -1dx3y + 2dx3y = 0

Combine like terms: 1dxy + -1dxy = 0

-1adx4 + 0 + -1dx3y + 2dx3y = 0

-1adx4 + -1dx3y + 2dx3y = 0

Combine like terms: -1dx3y + 2dx3y = 1dx3y

-1adx4 + 1dx3y = 0

Solving

-1adx4 + 1dx3y = 0

Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.

Add '-1dx3y' to each side of the equation.

-1adx4 + 1dx3y + -1dx3y = 0 + -1dx3y

Combine like terms: 1dx3y + -1dx3y = 0

-1adx4 + 0 = 0 + -1dx3y

-1adx4 = 0 + -1dx3y

Remove the zero:

-1adx4 = -1dx3y

Divide each side by '-1dx4'.

a = x-1y

Simplifying

a = x-1y