(6x+y+1)dx+(10y+x+1)dy=0
Answers
Simplifying
(6x2 + y + -1) * dx + -1(10y + -1x) * dy = 0
Reorder the terms:
(-1 + 6x2 + y) * dx + -1(10y + -1x) * dy = 0
Reorder the terms for easier multiplication:
dx(-1 + 6x2 + y) + -1(10y + -1x) * dy = 0
(-1 * dx + 6x2 * dx + y * dx) + -1(10y + -1x) * dy = 0
Reorder the terms:
(-1dx + dxy + 6dx3) + -1(10y + -1x) * dy = 0
(-1dx + dxy + 6dx3) + -1(10y + -1x) * dy = 0
Reorder the terms:
-1dx + dxy + 6dx3 + -1(-1x + 10y) * dy = 0
Reorder the terms for easier multiplication:
-1dx + dxy + 6dx3 + -1dy(-1x + 10y) = 0
-1dx + dxy + 6dx3 + (-1x * -1dy + 10y * -1dy) = 0
-1dx + dxy + 6dx3 + (1dxy + -10dy2) = 0
Reorder the terms:
-1dx + dxy + 1dxy + 6dx3 + -10dy2 = 0
Combine like terms: dxy + 1dxy = 2dxy
-1dx + 2dxy + 6dx3 + -10dy2 = 0
Solving
-1dx + 2dxy + 6dx3 + -10dy2 = 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(-1x + 2xy + 6x3 + -10y2) = 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 '(-1x + 2xy + 6x3 + -10y2)' equal to zero and attempt to solve:
Simplifying
-1x + 2xy + 6x3 + -10y2 = 0
Solving
-1x + 2xy + 6x3 + -10y2 = 0
Move all terms containing d to the left, all other terms to the right.
Add 'x' to each side of the equation.
-1x + 2xy + 6x3 + x + -10y2 = 0 + x
Reorder the terms:
-1x + x + 2xy + 6x3 + -10y2 = 0 + x
Combine like terms: -1x + x = 0
0 + 2xy + 6x3 + -10y2 = 0 + x
2xy + 6x3 + -10y2 = 0 + x
Remove the zero:
2xy + 6x3 + -10y2 = x
Add '-2xy' to each side of the equation.
2xy + 6x3 + -2xy + -10y2 = x + -2xy
Reorder the terms:
2xy + -2xy + 6x3 + -10y2 = x + -2xy
Combine like terms: 2xy + -2xy = 0
0 + 6x3 + -10y2 = x + -2xy
6x3 + -10y2 = x + -2xy
Add '-6x3' to each side of the equation.
6x3 + -6x3 + -10y2 = x + -2xy + -6x3
Combine like terms: 6x3 + -6x3 = 0
0 + -10y2 = x + -2xy + -6x3
-10y2 = x + -2xy + -6x3
Add '10y2' to each side of the equation.
-10y2 + 10y2 = x + -2xy + -6x3 + 10y2
Combine like terms: -10y2 + 10y2 = 0
0 = x + -2xy + -6x3 + 10y2
Simplifying
0 = x + -2xy + -6x3 + 10y2
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}
Hope It Helps You.