(2xy^3+y(cosx))dx+(3x^2y^2+(senx))dy=0

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Solution for (2xy^3+y(cosx))dx+(3x^2y^2+(senx))dy=0 equation: 


Simplifying
(2xy3 + y(cosx)) * dx + (3x2y2 + (senx)) * dy = 0

Multiply y * cosx
(2xy3 + cosxy) * dx + (3x2y2 + (senx)) * dy = 0

Reorder the terms:
(cosxy + 2xy3) * dx + (3x2y2 + (senx)) * dy = 0

Reorder the terms for easier multiplication:
dx(cosxy + 2xy3) + (3x2y2 + (senx)) * dy = 0
(cosxy * dx + 2xy3 * dx) + (3x2y2 + (senx)) * dy = 0
(cdosx2y + 2dx2y3) + (3x2y2 + (senx)) * dy = 0
cdosx2y + 2dx2y3 + (3x2y2 + ensx) * dy = 0

Reorder the terms:
cdosx2y + 2dx2y3 + (ensx + 3x2y2) * dy = 0

Reorder the terms for easier multiplication:
cdosx2y + 2dx2y3 + dy(ensx + 3x2y2) = 0
cdosx2y + 2dx2y3 + (ensx * dy + 3x2y2 * dy) = 0
cdosx2y + 2dx2y3 + (densxy + 3dx2y3) = 0

Reorder the terms:
cdosx2y + densxy + 2dx2y3 + 3dx2y3 = 0

Combine like terms: 2dx2y3 + 3dx2y3 = 5dx2y3
cdosx2y + densxy + 5dx2y3 = 0

Solving
cdosx2y + densxy + 5dx2y3 = 0

Solving for variable 'c'.

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

Add '-1densxy' to each side of the equation.
cdosx2y + densxy + -1densxy + 5dx2y3 = 0 + -1densxy

Combine like terms: densxy + -1densxy = 0
cdosx2y + 0 + 5dx2y3 = 0 + -1densxy
cdosx2y + 5dx2y3 = 0 + -1densxy
Remove the zero:
cdosx2y + 5dx2y3 = -1densxy

Add '-5dx2y3' to each side of the equation.
cdosx2y + 5dx2y3 + -5dx2y3 = -1densxy + -5dx2y3

Combine like terms: 5dx2y3 + -5dx2y3 = 0
cdosx2y + 0 = -1densxy + -5dx2y3
cdosx2y = -1densxy + -5dx2y3

Divide each side by 'dosx2y'.
c = -1eno-1x-1 + -5o-1s-1y2

Simplifying
c = -1eno-1x-1 + -5o-1s-1y2

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