(x^2+x(y^3))dx+(5(y^2)-xy+(y^3)siny)dy=0

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Solution for (x^2+x(y^3))dx+(5(y^2)-xy+(y^3)siny)dy=0 equation: 


Simplifying
(x2 + x(y3)) * dx + (5(y2) + -1xy + (y3) * siny) * dy = 0

Multiply x * y3
(x2 + xy3) * dx + (5(y2) + -1xy + (y3) * siny) * dy = 0

Reorder the terms:
(xy3 + x2) * dx + (5(y2) + -1xy + (y3) * siny) * dy = 0

Reorder the terms for easier multiplication:
dx(xy3 + x2) + (5(y2) + -1xy + (y3) * siny) * dy = 0
(xy3 * dx + x2 * dx) + (5(y2) + -1xy + (y3) * siny) * dy = 0
(dx2y3 + dx3) + (5(y2) + -1xy + (y3) * siny) * dy = 0

Multiply y3 * insy
dx2y3 + dx3 + (5y2 + -1xy + insy4) * dy = 0

Reorder the terms:
dx2y3 + dx3 + (insy4 + -1xy + 5y2) * dy = 0

Reorder the terms for easier multiplication:
dx2y3 + dx3 + dy(insy4 + -1xy + 5y2) = 0
dx2y3 + dx3 + (insy4 * dy + -1xy * dy + 5y2 * dy) = 0
dx2y3 + dx3 + (dinsy5 + -1dxy2 + 5dy3) = 0

Reorder the terms:
dinsy5 + -1dxy2 + dx2y3 + dx3 + 5dy3 = 0

Solving
dinsy5 + -1dxy2 + dx2y3 + dx3 + 5dy3 = 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), 'd'.
d(insy5 + -1xy2 + x2y3 + x3 + 5y3) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(insy5 + -1xy2 + x2y3 + x3 + 5y3)' equal to zero and attempt to solve:

Simplifying
insy5 + -1xy2 + x2y3 + x3 + 5y3 = 0

Solving
insy5 + -1xy2 + x2y3 + x3 + 5y3 = 0

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

Add '-1insy5' to each side of the equation.
insy5 + -1xy2 + x2y3 + x3 + -1insy5 + 5y3 = 0 + -1insy5

Reorder the terms:
insy5 + -1insy5 + -1xy2 + x2y3 + x3 + 5y3 = 0 + -1insy5

Combine like terms: insy5 + -1insy5 = 0
0 + -1xy2 + x2y3 + x3 + 5y3 = 0 + -1insy5
-1xy2 + x2y3 + x3 + 5y3 = 0 + -1insy5
Remove the zero:
-1xy2 + x2y3 + x3 + 5y3 = -1insy5

Add 'xy2' to each side of the equation.
-1xy2 + x2y3 + x3 + xy2 + 5y3 = -1insy5 + xy2

Reorder the terms:
-1xy2 + xy2 + x2y3 + x3 + 5y3 = -1insy5 + xy2

Combine like terms: -1xy2 + xy2 = 0
0 + x2y3 + x3 + 5y3 = -1insy5 + xy2
x2y3 + x3 + 5y3 = -1insy5 + xy2

Add '-1x2y3' to each side of the equation.
x2y3 + x3 + -1x2y3 + 5y3 = -1insy5 + xy2 + -1x2y3

Reorder the terms:
x2y3 + -1x2y3 + x3 + 5y3 = -1insy5 + xy2 + -1x2y3

Combine like terms: x2y3 + -1x2y3 = 0
0 + x3 + 5y3 = -1insy5 + xy2 + -1x2y3
x3 + 5y3 = -1insy5 + xy2 + -1x2y3

Add '-1x3' to each side of the equation.
x3 + -1x3 + 5y3 = -1insy5 + xy2 + -1x2y3 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 5y3 = -1insy5 + xy2 + -1x2y3 + -1x3
5y3 = -1insy5 + xy2 + -1x2y3 + -1x3

Add '-5y3' to each side of the equation.
5y3 + -5y3 = -1insy5 + xy2 + -1x2y3 + -1x3 + -5y3

Combine like terms: 5y3 + -5y3 = 0
0 = -1insy5 + xy2 + -1x2y3 + -1x3 + -5y3

Simplifying
0 = -1insy5 + xy2 + -1x2y3 + -1x3 + -5y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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