(x-y)(4x-y)dx+x(5x-y)dy=0

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Solution for (x-y)(4x-y)dx+x(5x-y)dy=0 equation: 


Simplifying
(x + -1y)(4x + -1y) * dx + x(5x + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(x + -1y)(4x + -1y) + x(5x + -1y) * dy = 0

Multiply (x + -1y) * (4x + -1y)
dx(x(4x + -1y) + -1y * (4x + -1y)) + x(5x + -1y) * dy = 0
dx((4x * x + -1y * x) + -1y * (4x + -1y)) + x(5x + -1y) * dy = 0

Reorder the terms:
dx((-1xy + 4x2) + -1y * (4x + -1y)) + x(5x + -1y) * dy = 0
dx((-1xy + 4x2) + -1y * (4x + -1y)) + x(5x + -1y) * dy = 0
dx(-1xy + 4x2 + (4x * -1y + -1y * -1y)) + x(5x + -1y) * dy = 0
dx(-1xy + 4x2 + (-4xy + 1y2)) + x(5x + -1y) * dy = 0

Reorder the terms:
dx(-1xy + -4xy + 4x2 + 1y2) + x(5x + -1y) * dy = 0

Combine like terms: -1xy + -4xy = -5xy
dx(-5xy + 4x2 + 1y2) + x(5x + -1y) * dy = 0
(-5xy * dx + 4x2 * dx + 1y2 * dx) + x(5x + -1y) * dy = 0

Reorder the terms:
(1dxy2 + -5dx2y + 4dx3) + x(5x + -1y) * dy = 0
(1dxy2 + -5dx2y + 4dx3) + x(5x + -1y) * dy = 0

Reorder the terms for easier multiplication:
1dxy2 + -5dx2y + 4dx3 + x * dy(5x + -1y) = 0

Multiply x * dy
1dxy2 + -5dx2y + 4dx3 + dxy(5x + -1y) = 0
1dxy2 + -5dx2y + 4dx3 + (5x * dxy + -1y * dxy) = 0

Reorder the terms:
1dxy2 + -5dx2y + 4dx3 + (-1dxy2 + 5dx2y) = 0
1dxy2 + -5dx2y + 4dx3 + (-1dxy2 + 5dx2y) = 0

Reorder the terms:
1dxy2 + -1dxy2 + -5dx2y + 5dx2y + 4dx3 = 0

Combine like terms: 1dxy2 + -1dxy2 = 0
0 + -5dx2y + 5dx2y + 4dx3 = 0
-5dx2y + 5dx2y + 4dx3 = 0

Combine like terms: -5dx2y + 5dx2y = 0
0 + 4dx3 = 0
4dx3 = 0

Solving
4dx3 = 0

Solving for variable 'd'.

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

Divide each side by '4'.
dx3 = 0

Simplifying
dx3 = 0

The solution to this equation could not be determined.

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