(4x-1y)dx+(-1x+4y)dy=0

Simple and best practice solution for (4x-1y)dx+(-1x+4y)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 (4x-1y)dx+(-1x+4y)dy=0 equation: 


Simplifying
(4x + -1y) * dx + (-1x + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(4x + -1y) + (-1x + 4y) * dy = 0
(4x * dx + -1y * dx) + (-1x + 4y) * dy = 0

Reorder the terms:
(-1dxy + 4dx2) + (-1x + 4y) * dy = 0
(-1dxy + 4dx2) + (-1x + 4y) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + 4dx2 + dy(-1x + 4y) = 0
-1dxy + 4dx2 + (-1x * dy + 4y * dy) = 0
-1dxy + 4dx2 + (-1dxy + 4dy2) = 0

Reorder the terms:
-1dxy + -1dxy + 4dx2 + 4dy2 = 0

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

Solving
-2dxy + 4dx2 + 4dy2 = 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(-1xy + 2x2 + 2y2) = 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 '(-1xy + 2x2 + 2y2)' equal to zero and attempt to solve:

Simplifying
-1xy + 2x2 + 2y2 = 0

Solving
-1xy + 2x2 + 2y2 = 0

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

Add 'xy' to each side of the equation.
-1xy + 2x2 + xy + 2y2 = 0 + xy

Reorder the terms:
-1xy + xy + 2x2 + 2y2 = 0 + xy

Combine like terms: -1xy + xy = 0
0 + 2x2 + 2y2 = 0 + xy
2x2 + 2y2 = 0 + xy
Remove the zero:
2x2 + 2y2 = xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 + 2y2 = xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 2y2 = xy + -2x2
2y2 = xy + -2x2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = xy + -2x2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = xy + -2x2 + -2y2

Simplifying
0 = xy + -2x2 + -2y2

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:

| b=vqk | | V=BQK | | -4(6x-3)+4=-24x+16 | | R=4t+8 | | 4x^2+x^3=1 | | -5x^3=10 | | 3/14-2/7=t | | gh-7=17 | | 8=-5(4x+3)+21x | | 3x^1+8x^2-3x^3=5 | | 3x+21y=-9 | | 3x+21y=9 | | 7/863/8 | | -8x-7=-5 | | 4(x+5)-(x-9)=1 | | 4s+2=10 | | 5+3x=11x+x | | 3/36 | | 6x-7=-8 | | v=ams | | 3(-2/3+4/9) | | 4=12n | | 10x^5-160x=0 | | 7w=4+9w | | 10x^2-160x=0 | | 5x^4-3x^2+15x^2-9=0 | | 3(6x-4[1+2x])+20=32 | | y=144x-18 | | y=-9x+72 | | y=20x+25 | | X-4/5-1=X-11/6 | | (3x^2+11x+6)/x+3 |

Equations solver categories