(2xy^3)*dx+y*cos(x)*dx+(3x^2)*(y^2)*dy+sin(x)*dy=0

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Solution for (2xy^3)*dx+y*cos(x)*dx+(3x^2)*(y^2)*dy+sin(x)*dy=0 equation: 


Simplifying
(2xy3) * dx + y * cos(x) * dx + (3x2)(y2) * dy + sin(x) * dy = 0

Remove parenthesis around (2xy3)
2xy3 * dx + y * cos(x) * dx + (3x2)(y2) * dy + sin(x) * dy = 0

Multiply xy3 * dx
2dx2y3 + y * cos(x) * dx + (3x2)(y2) * dy + sin(x) * dy = 0

Multiply y * cos
2dx2y3 + cosy * x * dx + (3x2)(y2) * dy + sin(x) * dy = 0

Multiply cosy * x
2dx2y3 + cosxy * dx + (3x2)(y2) * dy + sin(x) * dy = 0

Multiply cosxy * dx
2dx2y3 + cdosx2y + (3x2)(y2) * dy + sin(x) * dy = 0

Remove parenthesis around (3x2)
2dx2y3 + cdosx2y + 3x2(y2) * dy + sin(x) * dy = 0

Multiply x2 * y2
2dx2y3 + cdosx2y + 3x2y2 * dy + sin(x) * dy = 0

Multiply x2y2 * dy
2dx2y3 + cdosx2y + 3dx2y3 + sin(x) * dy = 0

Multiply ins * x
2dx2y3 + cdosx2y + 3dx2y3 + insx * dy = 0

Multiply insx * dy
2dx2y3 + cdosx2y + 3dx2y3 + dinsxy = 0

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

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

Solving
cdosx2y + dinsxy + 5dx2y3 = 0

Solving for variable 'c'.

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

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

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

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

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

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

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

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