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

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


Simplifying
(2xy + y + -1tan(y)) * dx + (x2 + -1xtan2(y) + sec2(y)) * dy = 0

Multiply ant * y
(2xy + y + -1anty) * dx + (x2 + -1xtan2(y) + sec2(y)) * dy = 0

Reorder the terms:
(-1anty + 2xy + y) * dx + (x2 + -1xtan2(y) + sec2(y)) * dy = 0

Reorder the terms for easier multiplication:
dx(-1anty + 2xy + y) + (x2 + -1xtan2(y) + sec2(y)) * dy = 0
(-1anty * dx + 2xy * dx + y * dx) + (x2 + -1xtan2(y) + sec2(y)) * dy = 0

Reorder the terms:
(-1adntxy + dxy + 2dx2y) + (x2 + -1xtan2(y) + sec2(y)) * dy = 0
(-1adntxy + dxy + 2dx2y) + (x2 + -1xtan2(y) + sec2(y)) * dy = 0

Multiply an2tx * y
-1adntxy + dxy + 2dx2y + (x2 + -1an2txy + sec2(y)) * dy = 0

Multiply c2es * y
-1adntxy + dxy + 2dx2y + (x2 + -1an2txy + c2esy) * dy = 0

Reorder the terms:
-1adntxy + dxy + 2dx2y + (-1an2txy + c2esy + x2) * dy = 0

Reorder the terms for easier multiplication:
-1adntxy + dxy + 2dx2y + dy(-1an2txy + c2esy + x2) = 0
-1adntxy + dxy + 2dx2y + (-1an2txy * dy + c2esy * dy + x2 * dy) = 0
-1adntxy + dxy + 2dx2y + (-1adn2txy2 + c2desy2 + dx2y) = 0

Reorder the terms:
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 2dx2y + dx2y = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = 0

Solving
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = 0

Solving for variable 'a'.

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

Add '-1c2desy2' to each side of the equation.
-1adntxy + -1adn2txy2 + c2desy2 + dxy + -1c2desy2 + 3dx2y = 0 + -1c2desy2

Reorder the terms:
-1adntxy + -1adn2txy2 + c2desy2 + -1c2desy2 + dxy + 3dx2y = 0 + -1c2desy2

Combine like terms: c2desy2 + -1c2desy2 = 0
-1adntxy + -1adn2txy2 + 0 + dxy + 3dx2y = 0 + -1c2desy2
-1adntxy + -1adn2txy2 + dxy + 3dx2y = 0 + -1c2desy2
Remove the zero:
-1adntxy + -1adn2txy2 + dxy + 3dx2y = -1c2desy2

Add '-1dxy' to each side of the equation.
-1adntxy + -1adn2txy2 + dxy + -1dxy + 3dx2y = -1c2desy2 + -1dxy

Combine like terms: dxy + -1dxy = 0
-1adntxy + -1adn2txy2 + 0 + 3dx2y = -1c2desy2 + -1dxy
-1adntxy + -1adn2txy2 + 3dx2y = -1c2desy2 + -1dxy

Add '-3dx2y' to each side of the equation.
-1adntxy + -1adn2txy2 + 3dx2y + -3dx2y = -1c2desy2 + -1dxy + -3dx2y

Combine like terms: 3dx2y + -3dx2y = 0
-1adntxy + -1adn2txy2 + 0 = -1c2desy2 + -1dxy + -3dx2y
-1adntxy + -1adn2txy2 = -1c2desy2 + -1dxy + -3dx2y

Reorder the terms:
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = -1c2desy2 + c2desy2 + -1dxy + dxy + -3dx2y + 3dx2y

Combine like terms: -1c2desy2 + c2desy2 = 0
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = 0 + -1dxy + dxy + -3dx2y + 3dx2y
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = -1dxy + dxy + -3dx2y + 3dx2y

Combine like terms: -1dxy + dxy = 0
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = 0 + -3dx2y + 3dx2y
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = -3dx2y + 3dx2y

Combine like terms: -3dx2y + 3dx2y = 0
-1adntxy + -1adn2txy2 + c2desy2 + dxy + 3dx2y = 0

Factor out the Greatest Common Factor (GCF), 'dy'.
dy(-1antx + -1an2txy + c2esy + x + 3x2) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Add '-1dy' to each side of the equation.
dy + -1dy = 0 + -1dy
Remove the zero:
0 = -1dy

Simplifying
0 = -1dy

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1antx + -1an2txy + c2esy + x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1antx + -1an2txy + c2esy + x + 3x2 = 0

Solving
-1antx + -1an2txy + c2esy + x + 3x2 = 0

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

Add '-1c2esy' to each side of the equation.
-1antx + -1an2txy + c2esy + x + -1c2esy + 3x2 = 0 + -1c2esy

Reorder the terms:
-1antx + -1an2txy + c2esy + -1c2esy + x + 3x2 = 0 + -1c2esy

Combine like terms: c2esy + -1c2esy = 0
-1antx + -1an2txy + 0 + x + 3x2 = 0 + -1c2esy
-1antx + -1an2txy + x + 3x2 = 0 + -1c2esy
Remove the zero:
-1antx + -1an2txy + x + 3x2 = -1c2esy

Add '-1x' to each side of the equation.
-1antx + -1an2txy + x + -1x + 3x2 = -1c2esy + -1x

Combine like terms: x + -1x = 0
-1antx + -1an2txy + 0 + 3x2 = -1c2esy + -1x
-1antx + -1an2txy + 3x2 = -1c2esy + -1x

Add '-3x2' to each side of the equation.
-1antx + -1an2txy + 3x2 + -3x2 = -1c2esy + -1x + -3x2

Combine like terms: 3x2 + -3x2 = 0
-1antx + -1an2txy + 0 = -1c2esy + -1x + -3x2
-1antx + -1an2txy = -1c2esy + -1x + -3x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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