x(tan^2y)*dy+x*dy=(2x^2+tany)dx

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Solution for x(tan^2y)*dy+x*dy=(2x^2+tany)dx equation: 


Simplifying
x(tan2y) * dy + x * dy = (2x2 + tany) * dx

Multiply x * an2ty
an2txy * dy + x * dy = (2x2 + tany) * dx

Multiply an2txy * dy
adn2txy2 + x * dy = (2x2 + tany) * dx

Multiply x * dy
adn2txy2 + dxy = (2x2 + tany) * dx

Reorder the terms:
adn2txy2 + dxy = (anty + 2x2) * dx

Reorder the terms for easier multiplication:
adn2txy2 + dxy = dx(anty + 2x2)
adn2txy2 + dxy = (anty * dx + 2x2 * dx)
adn2txy2 + dxy = (adntxy + 2dx3)

Solving
adn2txy2 + dxy = adntxy + 2dx3

Solving for variable 'a'.

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

Add '-1adntxy' to each side of the equation.
adn2txy2 + -1adntxy + dxy = adntxy + -1adntxy + 2dx3

Reorder the terms:
-1adntxy + adn2txy2 + dxy = adntxy + -1adntxy + 2dx3

Combine like terms: adntxy + -1adntxy = 0
-1adntxy + adn2txy2 + dxy = 0 + 2dx3
-1adntxy + adn2txy2 + dxy = 2dx3

Add '-1dxy' to each side of the equation.
-1adntxy + adn2txy2 + dxy + -1dxy = -1dxy + 2dx3

Combine like terms: dxy + -1dxy = 0
-1adntxy + adn2txy2 + 0 = -1dxy + 2dx3
-1adntxy + adn2txy2 = -1dxy + 2dx3

Reorder the terms:
-1adntxy + adn2txy2 + dxy + -2dx3 = -1dxy + dxy + 2dx3 + -2dx3

Combine like terms: -1dxy + dxy = 0
-1adntxy + adn2txy2 + dxy + -2dx3 = 0 + 2dx3 + -2dx3
-1adntxy + adn2txy2 + dxy + -2dx3 = 2dx3 + -2dx3

Combine like terms: 2dx3 + -2dx3 = 0
-1adntxy + adn2txy2 + dxy + -2dx3 = 0

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(-1anty + an2ty2 + y + -2x2) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

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

Simplifying
0 = -1dx

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 '(-1anty + an2ty2 + y + -2x2)' equal to zero and attempt to solve:

Simplifying
-1anty + an2ty2 + y + -2x2 = 0

Reorder the terms:
-1anty + an2ty2 + -2x2 + y = 0

Solving
-1anty + an2ty2 + -2x2 + y = 0

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

Add '2x2' to each side of the equation.
-1anty + an2ty2 + -2x2 + 2x2 + y = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-1anty + an2ty2 + 0 + y = 0 + 2x2
-1anty + an2ty2 + y = 0 + 2x2
Remove the zero:
-1anty + an2ty2 + y = 2x2

Add '-1y' to each side of the equation.
-1anty + an2ty2 + y + -1y = 2x2 + -1y

Combine like terms: y + -1y = 0
-1anty + an2ty2 + 0 = 2x2 + -1y
-1anty + an2ty2 = 2x2 + -1y

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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