(ysinx+(x)ycosx)dx+((x)sinx+1)dy=0

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Solution for (ysinx+(x)ycosx)dx+((x)sinx+1)dy=0 equation: 


Simplifying
(ysinx + (x) * ycosx) * dx + ((x) * sinx + 1) * dy = 0

Multiply x * cosxy
(insxy + cosx2y) * dx + ((x) * sinx + 1) * dy = 0

Reorder the terms:
(cosx2y + insxy) * dx + ((x) * sinx + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(cosx2y + insxy) + ((x) * sinx + 1) * dy = 0
(cosx2y * dx + insxy * dx) + ((x) * sinx + 1) * dy = 0
(cdosx3y + dinsx2y) + ((x) * sinx + 1) * dy = 0

Multiply x * insx
cdosx3y + dinsx2y + (insx2 + 1) * dy = 0

Reorder the terms:
cdosx3y + dinsx2y + (1 + insx2) * dy = 0

Reorder the terms for easier multiplication:
cdosx3y + dinsx2y + dy(1 + insx2) = 0
cdosx3y + dinsx2y + (1 * dy + insx2 * dy) = 0

Reorder the terms:
cdosx3y + dinsx2y + (dinsx2y + 1dy) = 0
cdosx3y + dinsx2y + (dinsx2y + 1dy) = 0

Combine like terms: dinsx2y + dinsx2y = 2dinsx2y
cdosx3y + 2dinsx2y + 1dy = 0

Solving
cdosx3y + 2dinsx2y + 1dy = 0

Solving for variable 'c'.

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

Add '-2dinsx2y' to each side of the equation.
cdosx3y + 2dinsx2y + -2dinsx2y + 1dy = 0 + -2dinsx2y

Combine like terms: 2dinsx2y + -2dinsx2y = 0
cdosx3y + 0 + 1dy = 0 + -2dinsx2y
cdosx3y + 1dy = 0 + -2dinsx2y
Remove the zero:
cdosx3y + 1dy = -2dinsx2y

Add '-1dy' to each side of the equation.
cdosx3y + 1dy + -1dy = -2dinsx2y + -1dy

Combine like terms: 1dy + -1dy = 0
cdosx3y + 0 = -2dinsx2y + -1dy
cdosx3y = -2dinsx2y + -1dy

Divide each side by 'dosx3y'.
c = -2ino-1x-1 + -1o-1s-1x-3

Simplifying
c = -2ino-1x-1 + -1o-1s-1x-3

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