(Yln(y)-2xy)dx+(x+y)dy=0

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Solution for (Yln(y)-2xy)dx+(x+y)dy=0 equation: 


Simplifying
(Yln(y) + -2xy) * dx + (x + y) * dy = 0

Multiply lnY * y
(lnyY + -2xy) * dx + (x + y) * dy = 0

Reorder the terms for easier multiplication:
dx(lnyY + -2xy) + (x + y) * dy = 0
(lnyY * dx + -2xy * dx) + (x + y) * dy = 0
(dlnxyY + -2dx2y) + (x + y) * dy = 0

Reorder the terms for easier multiplication:
dlnxyY + -2dx2y + dy(x + y) = 0
dlnxyY + -2dx2y + (x * dy + y * dy) = 0
dlnxyY + -2dx2y + (dxy + dy2) = 0

Reorder the terms:
dlnxyY + dxy + -2dx2y + dy2 = 0

Solving
dlnxyY + dxy + -2dx2y + dy2 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'dy'.
dy(lnxY + x + -2x2 + y) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(lnxY + x + -2x2 + y)' equal to zero and attempt to solve:

Simplifying
lnxY + x + -2x2 + y = 0

Solving
lnxY + x + -2x2 + y = 0

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

Add '-1lnxY' to each side of the equation.
lnxY + x + -2x2 + -1lnxY + y = 0 + -1lnxY

Reorder the terms:
lnxY + -1lnxY + x + -2x2 + y = 0 + -1lnxY

Combine like terms: lnxY + -1lnxY = 0
0 + x + -2x2 + y = 0 + -1lnxY
x + -2x2 + y = 0 + -1lnxY
Remove the zero:
x + -2x2 + y = -1lnxY

Add '-1x' to each side of the equation.
x + -2x2 + -1x + y = -1lnxY + -1x

Reorder the terms:
x + -1x + -2x2 + y = -1lnxY + -1x

Combine like terms: x + -1x = 0
0 + -2x2 + y = -1lnxY + -1x
-2x2 + y = -1lnxY + -1x

Add '2x2' to each side of the equation.
-2x2 + 2x2 + y = -1lnxY + -1x + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + y = -1lnxY + -1x + 2x2
y = -1lnxY + -1x + 2x2

Add '-1y' to each side of the equation.
y + -1y = -1lnxY + -1x + 2x2 + -1y

Combine like terms: y + -1y = 0
0 = -1lnxY + -1x + 2x2 + -1y

Simplifying
0 = -1lnxY + -1x + 2x2 + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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