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

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


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

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

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

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

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

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

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

Simplifying
4xy + -1x2 + y2 = 0

Solving
4xy + -1x2 + y2 = 0

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

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

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

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

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

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

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

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

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

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:

| 6(w-4)=8w-36 | | 7y+13=5y+4 | | 21=5y+2y | | 2x=-5x-2/11 | | m^2+2m-29=0 | | f(5)=3x+1 | | -5(3-z)=x+1 | | 24=2y+4y | | 2m^2=16 | | (8j+3)(j-2)=0 | | 15x-2y=44 | | 11a*2-18a= | | 11-u=157 | | 8-(-4)+5= | | m^2+4m-89=0 | | k^2-10k-17=0 | | n^2+2n-77=0 | | 60/84=b/7 | | 2ln(2x-3)+6=0 | | (3n+7)(n-9)=0 | | -2=5r+3r | | m^2+20m+84=0 | | 5/6=3x-4/7 | | n^2+10n-37=0 | | (2/3)^2x(18/15)^-2 | | p^2+12p-40=0 | | (h-4)(h+2)=0 | | x=(450x2x)/100 | | 2x^2+9x+15=0 | | 5y-4x+2y= | | 4m-17=31-2m | | Y=120-15x |

Equations solver categories