(2x+2y)dx+(2x-ky)dy=0

Simple and best practice solution for (2x+2y)dx+(2x-ky)dy=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (2x+2y)dx+(2x-ky)dy=0 equation: 


Simplifying
(2x + 2y) * dx + (2x + -1ky) * dy = 0

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

Reorder the terms:
(2dxy + 2dx2) + (2x + -1ky) * dy = 0
(2dxy + 2dx2) + (2x + -1ky) * dy = 0

Reorder the terms:
2dxy + 2dx2 + (-1ky + 2x) * dy = 0

Reorder the terms for easier multiplication:
2dxy + 2dx2 + dy(-1ky + 2x) = 0
2dxy + 2dx2 + (-1ky * dy + 2x * dy) = 0
2dxy + 2dx2 + (-1dky2 + 2dxy) = 0

Reorder the terms:
-1dky2 + 2dxy + 2dxy + 2dx2 = 0

Combine like terms: 2dxy + 2dxy = 4dxy
-1dky2 + 4dxy + 2dx2 = 0

Solving
-1dky2 + 4dxy + 2dx2 = 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(-1ky2 + 4xy + 2x2) = 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 '(-1ky2 + 4xy + 2x2)' equal to zero and attempt to solve:

Simplifying
-1ky2 + 4xy + 2x2 = 0

Solving
-1ky2 + 4xy + 2x2 = 0

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

Add 'ky2' to each side of the equation.
-1ky2 + 4xy + ky2 + 2x2 = 0 + ky2

Reorder the terms:
-1ky2 + ky2 + 4xy + 2x2 = 0 + ky2

Combine like terms: -1ky2 + ky2 = 0
0 + 4xy + 2x2 = 0 + ky2
4xy + 2x2 = 0 + ky2
Remove the zero:
4xy + 2x2 = ky2

Add '-4xy' to each side of the equation.
4xy + -4xy + 2x2 = ky2 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 2x2 = ky2 + -4xy
2x2 = ky2 + -4xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 = ky2 + -4xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 = ky2 + -4xy + -2x2

Simplifying
0 = ky2 + -4xy + -2x2

The solution to this equation could not be determined.

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

See similar equations:

| 2x^(2/3)-9x^(1/3)=5 | | c-5=5-2 | | -x/2=1/3 | | x+(x*2)+(x+4)=24 | | t+9t+20=0 | | 54+z^2=0 | | -12+20y=-24 | | -40=14x-4x | | 1u-1v=3 | | -40=14x+4x | | Sin^2(1/2x)-1/4=0 | | 125=200p | | 9x+144=8x+144 | | x^2+12x-128=0 | | y=0.4(0.0)+8.2 | | 20x+8(18-x)=288 | | -10m+5m=-35 | | 4.5x=0.0 | | 56x^2-5x+2=0 | | 4a=398 | | 15.5x+2.5= | | 5x(x^2)=126 | | (46-3x)+(112-21x)+(78-12x)=180 | | 3(0)+9y=-9 | | 2(x-6)=y-2 | | 4m+6=-8 | | (6x-9)+(3x)+(x)=180 | | 4p=183 | | (6x-15)+(3x)+(x)=180 | | w-3(w-9)= | | 18(r+39)=792 | | log(5x-2)=-1log(x+2) |

Equations solver categories