(2x^2+3y)dx-(3x+4y^4)dy=0

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


Simplifying
(2x2 + 3y) * dx + -1(3x + 4y4) * dy = 0

Reorder the terms for easier multiplication:
dx(2x2 + 3y) + -1(3x + 4y4) * dy = 0
(2x2 * dx + 3y * dx) + -1(3x + 4y4) * dy = 0

Reorder the terms:
(3dxy + 2dx3) + -1(3x + 4y4) * dy = 0
(3dxy + 2dx3) + -1(3x + 4y4) * dy = 0

Reorder the terms for easier multiplication:
3dxy + 2dx3 + -1dy(3x + 4y4) = 0
3dxy + 2dx3 + (3x * -1dy + 4y4 * -1dy) = 0
3dxy + 2dx3 + (-3dxy + -4dy5) = 0

Reorder the terms:
3dxy + -3dxy + 2dx3 + -4dy5 = 0

Combine like terms: 3dxy + -3dxy = 0
0 + 2dx3 + -4dy5 = 0
2dx3 + -4dy5 = 0

Solving
2dx3 + -4dy5 = 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), '2d'.
2d(x3 + -2y5) = 0

Ignore the factor 2.

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 '(x3 + -2y5)' equal to zero and attempt to solve:

Simplifying
x3 + -2y5 = 0

Solving
x3 + -2y5 = 0

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

Add '-1x3' to each side of the equation.
x3 + -1x3 + -2y5 = 0 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + -2y5 = 0 + -1x3
-2y5 = 0 + -1x3
Remove the zero:
-2y5 = -1x3

Add '2y5' to each side of the equation.
-2y5 + 2y5 = -1x3 + 2y5

Combine like terms: -2y5 + 2y5 = 0
0 = -1x3 + 2y5

Simplifying
0 = -1x3 + 2y5

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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