(2xcosy+3x^2y)dx+(x^3-x^2seny-y)dy=0

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Solution for (2xcosy+3x^2y)dx+(x^3-x^2seny-y)dy=0 equation: 


Simplifying
(2xcosy + 3x2y) * dx + (x3 + -1x2seny + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(2cosxy + 3x2y) + (x3 + -1x2seny + -1y) * dy = 0
(2cosxy * dx + 3x2y * dx) + (x3 + -1x2seny + -1y) * dy = 0
(2cdosx2y + 3dx3y) + (x3 + -1x2seny + -1y) * dy = 0

Reorder the terms:
2cdosx2y + 3dx3y + (-1ensx2y + x3 + -1y) * dy = 0

Reorder the terms for easier multiplication:
2cdosx2y + 3dx3y + dy(-1ensx2y + x3 + -1y) = 0
2cdosx2y + 3dx3y + (-1ensx2y * dy + x3 * dy + -1y * dy) = 0
2cdosx2y + 3dx3y + (-1densx2y2 + dx3y + -1dy2) = 0

Reorder the terms:
2cdosx2y + -1densx2y2 + 3dx3y + dx3y + -1dy2 = 0

Combine like terms: 3dx3y + dx3y = 4dx3y
2cdosx2y + -1densx2y2 + 4dx3y + -1dy2 = 0

Solving
2cdosx2y + -1densx2y2 + 4dx3y + -1dy2 = 0

Solving for variable 'c'.

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

Add 'densx2y2' to each side of the equation.
2cdosx2y + -1densx2y2 + 4dx3y + densx2y2 + -1dy2 = 0 + densx2y2

Reorder the terms:
2cdosx2y + -1densx2y2 + densx2y2 + 4dx3y + -1dy2 = 0 + densx2y2

Combine like terms: -1densx2y2 + densx2y2 = 0
2cdosx2y + 0 + 4dx3y + -1dy2 = 0 + densx2y2
2cdosx2y + 4dx3y + -1dy2 = 0 + densx2y2
Remove the zero:
2cdosx2y + 4dx3y + -1dy2 = densx2y2

Add '-4dx3y' to each side of the equation.
2cdosx2y + 4dx3y + -4dx3y + -1dy2 = densx2y2 + -4dx3y

Combine like terms: 4dx3y + -4dx3y = 0
2cdosx2y + 0 + -1dy2 = densx2y2 + -4dx3y
2cdosx2y + -1dy2 = densx2y2 + -4dx3y

Add 'dy2' to each side of the equation.
2cdosx2y + -1dy2 + dy2 = densx2y2 + -4dx3y + dy2

Combine like terms: -1dy2 + dy2 = 0
2cdosx2y + 0 = densx2y2 + -4dx3y + dy2
2cdosx2y = densx2y2 + -4dx3y + dy2

Divide each side by '2dosx2y'.
c = 0.5eno-1y + -2o-1s-1x + 0.5o-1s-1x-2y

Simplifying
c = 0.5eno-1y + -2o-1s-1x + 0.5o-1s-1x-2y

Reorder the terms:
c = 0.5eno-1y + 0.5o-1s-1x-2y + -2o-1s-1x

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