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

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


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

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

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

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

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

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + dx2 + -1dy2 = 0

Solving
4dxy + dx2 + -1dy2 = 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(4xy + x2 + -1y2) = 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 '(4xy + x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
4xy + x2 + -1y2 = 0

Solving
4xy + x2 + -1y2 = 0

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

Add '-4xy' to each side of the equation.
4xy + x2 + -4xy + -1y2 = 0 + -4xy

Reorder the terms:
4xy + -4xy + x2 + -1y2 = 0 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + x2 + -1y2 = 0 + -4xy
x2 + -1y2 = 0 + -4xy
Remove the zero:
x2 + -1y2 = -4xy

Add '-1x2' to each side of the equation.
x2 + -1x2 + -1y2 = -4xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -1y2 = -4xy + -1x2
-1y2 = -4xy + -1x2

Add 'y2' to each side of the equation.
-1y2 + y2 = -4xy + -1x2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -4xy + -1x2 + y2

Simplifying
0 = -4xy + -1x2 + y2

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:

| 8r-(5-3r)=5+r | | 11*1/22 | | 14+16(m+6)=-8 | | 18x^2+22x+21=0 | | -56=-20-6x | | 9k+35=4k | | 5(-10-6x)=70 | | -34=20-9x | | B=67-34+15 | | (3x-3)(5x-6)=0 | | 190=-y+92 | | -3(-2x+8)=18 | | 3.3x+52.2=18.0-8.1x | | -17-3x=-44 | | 69-u=176 | | 2(-4x+7)=86 | | 40=-w+295 | | 45+11x=133 | | 37=28-2c | | 0.00000000000000002=x(x+0.1) | | -5(-1.25)-y=21 | | 7(4x+8)=252 | | 66+7x=157 | | -w+64=182 | | 4/3×3.14×1.5^3 | | w^2-5w+20=0 | | -4+7x+4x=64 | | (2x^2+3x)+(5x^2+5)+(6x^2+3x+5)=0 | | 13.2y=38.6 | | 0=3+10x | | (3x-10)=(x+6) | | 4n^2-4n+6=0 |

Equations solver categories