(x-y)dx+tan(x)dy=0

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Solution for (x-y)dx+tan(x)dy=0 equation:


Simplifying
(x + -1y) * dx + tan(x) * dy = 0

Reorder the terms for easier multiplication:
dx(x + -1y) + tan(x) * dy = 0
(x * dx + -1y * dx) + tan(x) * dy = 0

Reorder the terms:
(-1dxy + dx2) + tan(x) * dy = 0
(-1dxy + dx2) + tan(x) * dy = 0

Multiply ant * x
-1dxy + dx2 + antx * dy = 0

Multiply antx * dy
-1dxy + dx2 + adntxy = 0

Reorder the terms:
adntxy + -1dxy + dx2 = 0

Solving
adntxy + -1dxy + dx2 = 0

Solving for variable 'a'.

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

Add 'dxy' to each side of the equation.
adntxy + -1dxy + dxy + dx2 = 0 + dxy

Combine like terms: -1dxy + dxy = 0
adntxy + 0 + dx2 = 0 + dxy
adntxy + dx2 = 0 + dxy
Remove the zero:
adntxy + dx2 = dxy

Add '-1dx2' to each side of the equation.
adntxy + dx2 + -1dx2 = dxy + -1dx2

Combine like terms: dx2 + -1dx2 = 0
adntxy + 0 = dxy + -1dx2
adntxy = dxy + -1dx2

Divide each side by 'dntxy'.
a = n-1t-1 + -1n-1t-1xy-1

Simplifying
a = n-1t-1 + -1n-1t-1xy-1

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