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

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


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

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

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

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

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

Combine like terms: dxy + dxy = 2dxy
2dxy + 2dx2 + 2dy2 = 0

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

Simplifying
xy + x2 + y2 = 0

Solving
xy + x2 + y2 = 0

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

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

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

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

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

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

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

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

Simplifying
0 = -1xy + -1x2 + -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:

| -6k+13=-3k-5 | | -3v+1=3v+31 | | xz-4Y^2xz=0 | | 9q+7=4q-13 | | -3x-12=18 | | 56x^2+8x-64=0 | | 7m+65=2 | | -2b-5=-5b+1 | | -c+3=3c-5 | | 2(y-5)=14 | | 6n^2-41n-7=0 | | 7g-3=3+6g | | q+7=5q-1 | | -16=x^2 | | 4w-3=2w-7 | | -6t+1=-t+6 | | yz-2x^2yz=0 | | 6x-2=11x-12 | | -9+10g=54 | | -3b+21=-8b+6 | | 3p^2+25p+8=0 | | 8x-15+3x=7 | | 9n^2=10-3n+8n^2 | | -4n-5=-5 | | 3.5=0.25k-1.25 | | 3f-3=8f-3 | | 86+2z=256-9z | | 4x-24=-6(x-6) | | -4r-19=1 | | (2y^3+8y^2+1)+(3y^3-y-4)= | | 7x^2+7x=-10+6x^2 | | 86+2z=200 |

Equations solver categories