(2x-y)dx+(x+6y)dy=0

Simple and best practice solution for (2x-y)dx+(x+6y)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-y)dx+(x+6y)dy=0 equation: 


Simplifying
(2x + -1y) * dx + (x + 6y) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + -1y) + (x + 6y) * dy = 0
(2x * dx + -1y * dx) + (x + 6y) * dy = 0

Reorder the terms:
(-1dxy + 2dx2) + (x + 6y) * dy = 0
(-1dxy + 2dx2) + (x + 6y) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + 2dx2 + dy(x + 6y) = 0
-1dxy + 2dx2 + (x * dy + 6y * dy) = 0
-1dxy + 2dx2 + (dxy + 6dy2) = 0

Reorder the terms:
-1dxy + dxy + 2dx2 + 6dy2 = 0

Combine like terms: -1dxy + dxy = 0
0 + 2dx2 + 6dy2 = 0
2dx2 + 6dy2 = 0

Solving
2dx2 + 6dy2 = 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(x2 + 3y2) = 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 '(x2 + 3y2)' equal to zero and attempt to solve:

Simplifying
x2 + 3y2 = 0

Solving
x2 + 3y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 + 3y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 3y2 = 0 + -1x2
3y2 = 0 + -1x2
Remove the zero:
3y2 = -1x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -1x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -1x2 + -3y2

Simplifying
0 = -1x2 + -3y2

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:

| x=y-1.75 | | Y-9=-1/5(10) | | 7t+4t=50-14+8 | | y=(-3)-1 | | Tan^3x-tan^2x-3tanx-3=0 | | 5x-6(y)=33 | | 24/4x-4=6/x | | 25a^3-9a=0 | | 20=-16t^2+5t+15 | | 25x^2-25x+4= | | F(12)=4 | | 7(a+4)=3(3+3a) | | 2a-4=5+5a | | b/8=8/16 | | 18+6a=4a | | 4x=3.5x+35 | | 4x=2.5x+35 | | Cos(2x)+7cos(x)=8 | | 4x+35=2.5x | | 12m^2+25m+7= | | 4x+35=3.5x | | 1+5y-21y= | | 0.8+0.8x^2-x=0 | | -2b-3-9b-5= | | 2x+1y-1.75=3.25 | | 12-(7x)+2x-(-12)= | | 2x-1.75+1y=3.25 | | Y-8=-3/7x | | 0.8x+0.5=4.5 | | (5r-3)(4r+2r+5)= | | Y-4=-1/3(x-2) | | y=-1-y |

Equations solver categories