(3x^2y+6xy+0.5y^2)dx+(3x^2+y)dy=0

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Solution for (3x^2y+6xy+0.5y^2)dx+(3x^2+y)dy=0 equation: 


Simplifying
(3x2y + 6xy + 0.5y2) * dx + (3x2 + y) * dy = 0

Reorder the terms:
(6xy + 3x2y + 0.5y2) * dx + (3x2 + y) * dy = 0

Reorder the terms for easier multiplication:
dx(6xy + 3x2y + 0.5y2) + (3x2 + y) * dy = 0
(6xy * dx + 3x2y * dx + 0.5y2 * dx) + (3x2 + y) * dy = 0

Reorder the terms:
(0.5dxy2 + 6dx2y + 3dx3y) + (3x2 + y) * dy = 0
(0.5dxy2 + 6dx2y + 3dx3y) + (3x2 + y) * dy = 0

Reorder the terms for easier multiplication:
0.5dxy2 + 6dx2y + 3dx3y + dy(3x2 + y) = 0
0.5dxy2 + 6dx2y + 3dx3y + (3x2 * dy + y * dy) = 0
0.5dxy2 + 6dx2y + 3dx3y + (3dx2y + dy2) = 0

Reorder the terms:
0.5dxy2 + 6dx2y + 3dx2y + 3dx3y + dy2 = 0

Combine like terms: 6dx2y + 3dx2y = 9dx2y
0.5dxy2 + 9dx2y + 3dx3y + dy2 = 0

Solving
0.5dxy2 + 9dx2y + 3dx3y + dy2 = 0

Solving for variable 'd'.

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

The solution to this equation could not be determined.

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