xtan^2(y)dy=(2x^2-x)dx+tanydx

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Solution for xtan^2(y)dy=(2x^2-x)dx+tanydx equation: 


Simplifying
xtan2(y) * dy = (2x2 + -1x) * dx + tanydx

Multiply an2tx * y
an2txy * dy = (2x2 + -1x) * dx + tanydx

Multiply an2txy * dy
adn2txy2 = (2x2 + -1x) * dx + tanydx

Reorder the terms:
adn2txy2 = (-1x + 2x2) * dx + tanydx

Reorder the terms for easier multiplication:
adn2txy2 = dx(-1x + 2x2) + tanydx
adn2txy2 = (-1x * dx + 2x2 * dx) + tanydx
adn2txy2 = (-1dx2 + 2dx3) + tanydx

Reorder the terms:
adn2txy2 = adntxy + -1dx2 + 2dx3

Solving
adn2txy2 = adntxy + -1dx2 + 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.
-1adntxy + adn2txy2 = adntxy + -1dx2 + -1adntxy + 2dx3

Reorder the terms:
-1adntxy + adn2txy2 = adntxy + -1adntxy + -1dx2 + 2dx3

Combine like terms: adntxy + -1adntxy = 0
-1adntxy + adn2txy2 = 0 + -1dx2 + 2dx3
-1adntxy + adn2txy2 = -1dx2 + 2dx3

Reorder the terms:
-1adntxy + adn2txy2 + dx2 + -2dx3 = -1dx2 + dx2 + 2dx3 + -2dx3

Combine like terms: -1dx2 + dx2 = 0
-1adntxy + adn2txy2 + dx2 + -2dx3 = 0 + 2dx3 + -2dx3
-1adntxy + adn2txy2 + dx2 + -2dx3 = 2dx3 + -2dx3

Combine like terms: 2dx3 + -2dx3 = 0
-1adntxy + adn2txy2 + dx2 + -2dx3 = 0

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(-1anty + an2ty2 + x + -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 + x + -2x2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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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