((x^3+15x^2+1)y)dx+((3y^4+y^5+5)x)dy=0

Solution for ((x^3+15x^2+1)y)dx+((3y^4+y^5+5)x)dy=0 equation:

Simplifying
((x3 + 15x2 + 1) * y) * dx + ((3y4 + y5 + 5) * x) * dy = 0

Reorder the terms:
((1 + 15x2 + x3) * y) * dx + ((3y4 + y5 + 5) * x) * dy = 0

Reorder the terms for easier multiplication:
(y(1 + 15x2 + x3)) * dx + ((3y4 + y5 + 5) * x) * dy = 0
((1 * y + 15x2 * y + x3 * y)) * dx + ((3y4 + y5 + 5) * x) * dy = 0

Reorder the terms:
((15x2y + x3y + 1y)) * dx + ((3y4 + y5 + 5) * x) * dy = 0
((15x2y + x3y + 1y)) * dx + ((3y4 + y5 + 5) * x) * dy = 0

Reorder the terms for easier multiplication:
dx(15x2y + x3y + 1y) + ((3y4 + y5 + 5) * x) * dy = 0
(15x2y * dx + x3y * dx + 1y * dx) + ((3y4 + y5 + 5) * x) * dy = 0

Reorder the terms:
(1dxy + 15dx3y + dx4y) + ((3y4 + y5 + 5) * x) * dy = 0
(1dxy + 15dx3y + dx4y) + ((3y4 + y5 + 5) * x) * dy = 0

Reorder the terms:
1dxy + 15dx3y + dx4y + ((5 + 3y4 + y5) * x) * dy = 0

Reorder the terms for easier multiplication:
1dxy + 15dx3y + dx4y + (x(5 + 3y4 + y5)) * dy = 0
1dxy + 15dx3y + dx4y + ((5 * x + 3y4 * x + y5 * x)) * dy = 0
1dxy + 15dx3y + dx4y + ((5x + 3xy4 + xy5)) * dy = 0

Reorder the terms for easier multiplication:
1dxy + 15dx3y + dx4y + dy(5x + 3xy4 + xy5) = 0
1dxy + 15dx3y + dx4y + (5x * dy + 3xy4 * dy + xy5 * dy) = 0
1dxy + 15dx3y + dx4y + (5dxy + 3dxy5 + dxy6) = 0

Reorder the terms:
1dxy + 5dxy + 3dxy5 + dxy6 + 15dx3y + dx4y = 0

Combine like terms: 1dxy + 5dxy = 6dxy
6dxy + 3dxy5 + dxy6 + 15dx3y + dx4y = 0

Solving
6dxy + 3dxy5 + dxy6 + 15dx3y + dx4y = 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(6 + 3y4 + y5 + 15x2 + x3) = 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 '(6 + 3y4 + y5 + 15x2 + x3)' equal to zero and attempt to solve:

Simplifying
6 + 3y4 + y5 + 15x2 + x3 = 0

Reorder the terms:
6 + 15x2 + x3 + 3y4 + y5 = 0

Solving
6 + 15x2 + x3 + 3y4 + y5 = 0

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

Add '-6' to each side of the equation.
6 + 15x2 + x3 + 3y4 + -6 + y5 = 0 + -6

Reorder the terms:
6 + -6 + 15x2 + x3 + 3y4 + y5 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 15x2 + x3 + 3y4 + y5 = 0 + -6
15x2 + x3 + 3y4 + y5 = 0 + -6

Combine like terms: 0 + -6 = -6
15x2 + x3 + 3y4 + y5 = -6

Add '-15x2' to each side of the equation.
15x2 + x3 + 3y4 + -15x2 + y5 = -6 + -15x2

Reorder the terms:
15x2 + -15x2 + x3 + 3y4 + y5 = -6 + -15x2

Combine like terms: 15x2 + -15x2 = 0
0 + x3 + 3y4 + y5 = -6 + -15x2
x3 + 3y4 + y5 = -6 + -15x2

Add '-1x3' to each side of the equation.
x3 + 3y4 + -1x3 + y5 = -6 + -15x2 + -1x3

Reorder the terms:
x3 + -1x3 + 3y4 + y5 = -6 + -15x2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 3y4 + y5 = -6 + -15x2 + -1x3
3y4 + y5 = -6 + -15x2 + -1x3

Add '-3y4' to each side of the equation.
3y4 + -3y4 + y5 = -6 + -15x2 + -1x3 + -3y4

Combine like terms: 3y4 + -3y4 = 0
0 + y5 = -6 + -15x2 + -1x3 + -3y4
y5 = -6 + -15x2 + -1x3 + -3y4

Add '-1y5' to each side of the equation.
y5 + -1y5 = -6 + -15x2 + -1x3 + -3y4 + -1y5

Combine like terms: y5 + -1y5 = 0
0 = -6 + -15x2 + -1x3 + -3y4 + -1y5

Simplifying
0 = -6 + -15x2 + -1x3 + -3y4 + -1y5

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.