(x*cos(y)-y*sen(y))dy+(x*sen(y)+y*cos(y))dx=0

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Solution for (x*cos(y)-y*sen(y))dy+(x*sen(y)+y*cos(y))dx=0 equation:


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

Multiply x * cos
(cosx * y + -1y * sen(y)) * dy + (x * sen(y) + y * cos(y)) * dx = 0

Multiply cosx * y
(cosxy + -1y * sen(y)) * dy + (x * sen(y) + y * cos(y)) * dx = 0

Multiply y * ens
(cosxy + -1ensy * y) * dy + (x * sen(y) + y * cos(y)) * dx = 0

Multiply ensy * y
(cosxy + -1ensy2) * dy + (x * sen(y) + y * cos(y)) * dx = 0

Reorder the terms for easier multiplication:
dy(cosxy + -1ensy2) + (x * sen(y) + y * cos(y)) * dx = 0
(cosxy * dy + -1ensy2 * dy) + (x * sen(y) + y * cos(y)) * dx = 0
(cdosxy2 + -1densy3) + (x * sen(y) + y * cos(y)) * dx = 0

Multiply x * ens
cdosxy2 + -1densy3 + (ensx * y + y * cos(y)) * dx = 0

Multiply ensx * y
cdosxy2 + -1densy3 + (ensxy + y * cos(y)) * dx = 0

Multiply y * cos
cdosxy2 + -1densy3 + (ensxy + cosy * y) * dx = 0

Multiply cosy * y
cdosxy2 + -1densy3 + (ensxy + cosy2) * dx = 0

Reorder the terms:
cdosxy2 + -1densy3 + (cosy2 + ensxy) * dx = 0

Reorder the terms for easier multiplication:
cdosxy2 + -1densy3 + dx(cosy2 + ensxy) = 0
cdosxy2 + -1densy3 + (cosy2 * dx + ensxy * dx) = 0
cdosxy2 + -1densy3 + (cdosxy2 + densx2y) = 0

Reorder the terms:
cdosxy2 + cdosxy2 + densx2y + -1densy3 = 0

Combine like terms: cdosxy2 + cdosxy2 = 2cdosxy2
2cdosxy2 + densx2y + -1densy3 = 0

Solving
2cdosxy2 + densx2y + -1densy3 = 0

Solving for variable 'c'.

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

Add '-1densx2y' to each side of the equation.
2cdosxy2 + densx2y + -1densx2y + -1densy3 = 0 + -1densx2y

Combine like terms: densx2y + -1densx2y = 0
2cdosxy2 + 0 + -1densy3 = 0 + -1densx2y
2cdosxy2 + -1densy3 = 0 + -1densx2y
Remove the zero:
2cdosxy2 + -1densy3 = -1densx2y

Add 'densy3' to each side of the equation.
2cdosxy2 + -1densy3 + densy3 = -1densx2y + densy3

Combine like terms: -1densy3 + densy3 = 0
2cdosxy2 + 0 = -1densx2y + densy3
2cdosxy2 = -1densx2y + densy3

Divide each side by '2dosxy2'.
c = -0.5eno-1xy-1 + 0.5eno-1x-1y

Simplifying
c = -0.5eno-1xy-1 + 0.5eno-1x-1y

Reorder the terms:
c = 0.5eno-1x-1y + -0.5eno-1xy-1

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