2ydx+x[x^2ln(y)-1]dy=0

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Solution for 2ydx+x[x^2ln(y)-1]dy=0 equation: 


Simplifying
2ydx + x[x2ln(y) + -1] * dy = 0

Multiply lnx2 * y
2dxy + x[lnx2y + -1] * dy = 0

Reorder the terms:
2dxy + x[-1 + lnx2y] * dy = 0

Reorder the terms for easier multiplication:
2dxy + x * dy[-1 + lnx2y] = 0

Multiply x * dy
2dxy + dxy[-1 + lnx2y] = 0
2dxy + [-1 * dxy + lnx2y * dxy] = 0

Reorder the terms:
2dxy + [dlnx3y2 + -1dxy] = 0
2dxy + [dlnx3y2 + -1dxy] = 0

Reorder the terms:
dlnx3y2 + 2dxy + -1dxy = 0

Combine like terms: 2dxy + -1dxy = 1dxy
dlnx3y2 + 1dxy = 0

Solving
dlnx3y2 + 1dxy = 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), 'dxy'.
dxy(lnx2y + 1) = 0


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

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 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 '(lnx2y + 1)' equal to zero and attempt to solve:

Simplifying
lnx2y + 1 = 0

Reorder the terms:
1 + lnx2y = 0

Solving
1 + lnx2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + lnx2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + lnx2y = 0 + -1
lnx2y = 0 + -1

Combine like terms: 0 + -1 = -1
lnx2y = -1

Add '-1lnx2y' to each side of the equation.
lnx2y + -1lnx2y = -1 + -1lnx2y

Combine like terms: lnx2y + -1lnx2y = 0
0 = -1 + -1lnx2y

Simplifying
0 = -1 + -1lnx2y

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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