(2xy-tany)dx+((x^2)-x((sec^2)y))dy=0

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Solution for (2xy-tany)dx+((x^2)-x((sec^2)y))dy=0 equation: 


Simplifying
(2xy + -1tany) * dx + ((x2) + -1x((sec2) * y)) * dy = 0

Reorder the terms:
(-1anty + 2xy) * dx + ((x2) + -1x((sec2) * y)) * dy = 0

Reorder the terms for easier multiplication:
dx(-1anty + 2xy) + ((x2) + -1x((sec2) * y)) * dy = 0
(-1anty * dx + 2xy * dx) + ((x2) + -1x((sec2) * y)) * dy = 0
(-1adntxy + 2dx2y) + ((x2) + -1x((sec2) * y)) * dy = 0
-1adntxy + 2dx2y + (x2 + -1x((sec2) * y)) * dy = 0

Multiply c2es * y
-1adntxy + 2dx2y + (x2 + -1x(c2esy)) * dy = 0

Multiply x * c2esy
-1adntxy + 2dx2y + (x2 + -1c2esxy) * dy = 0

Reorder the terms:
-1adntxy + 2dx2y + (-1c2esxy + x2) * dy = 0

Reorder the terms for easier multiplication:
-1adntxy + 2dx2y + dy(-1c2esxy + x2) = 0
-1adntxy + 2dx2y + (-1c2esxy * dy + x2 * dy) = 0
-1adntxy + 2dx2y + (-1c2desxy2 + dx2y) = 0

Reorder the terms:
-1adntxy + -1c2desxy2 + 2dx2y + dx2y = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
-1adntxy + -1c2desxy2 + 3dx2y = 0

Solving
-1adntxy + -1c2desxy2 + 3dx2y = 0

Solving for variable 'a'.

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

Add 'c2desxy2' to each side of the equation.
-1adntxy + -1c2desxy2 + c2desxy2 + 3dx2y = 0 + c2desxy2

Combine like terms: -1c2desxy2 + c2desxy2 = 0
-1adntxy + 0 + 3dx2y = 0 + c2desxy2
-1adntxy + 3dx2y = 0 + c2desxy2
Remove the zero:
-1adntxy + 3dx2y = c2desxy2

Add '-3dx2y' to each side of the equation.
-1adntxy + 3dx2y + -3dx2y = c2desxy2 + -3dx2y

Combine like terms: 3dx2y + -3dx2y = 0
-1adntxy + 0 = c2desxy2 + -3dx2y
-1adntxy = c2desxy2 + -3dx2y

Divide each side by '-1dntxy'.
a = -1c2en-1st-1y + 3n-1t-1x

Simplifying
a = -1c2en-1st-1y + 3n-1t-1x

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