(x^4+1)dy+x(1+4y^2)dx=0

Simple and best practice solution for (x^4+1)dy+x(1+4y^2)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 (x^4+1)dy+x(1+4y^2)dx=0 equation: 


Simplifying
(x4 + 1) * dy + x(1 + 4y2) * dx = 0

Reorder the terms:
(1 + x4) * dy + x(1 + 4y2) * dx = 0

Reorder the terms for easier multiplication:
dy(1 + x4) + x(1 + 4y2) * dx = 0
(1 * dy + x4 * dy) + x(1 + 4y2) * dx = 0

Reorder the terms:
(dx4y + 1dy) + x(1 + 4y2) * dx = 0
(dx4y + 1dy) + x(1 + 4y2) * dx = 0

Reorder the terms for easier multiplication:
dx4y + 1dy + x * dx(1 + 4y2) = 0

Multiply x * dx
dx4y + 1dy + dx2(1 + 4y2) = 0
dx4y + 1dy + (1 * dx2 + 4y2 * dx2) = 0
dx4y + 1dy + (1dx2 + 4dx2y2) = 0

Reorder the terms:
1dx2 + 4dx2y2 + dx4y + 1dy = 0

Solving
1dx2 + 4dx2y2 + dx4y + 1dy = 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(x2 + 4x2y2 + x4y + y) = 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 '(x2 + 4x2y2 + x4y + y)' equal to zero and attempt to solve:

Simplifying
x2 + 4x2y2 + x4y + y = 0

Solving
x2 + 4x2y2 + x4y + y = 0

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

Add '-1x2' to each side of the equation.
x2 + 4x2y2 + x4y + -1x2 + y = 0 + -1x2

Reorder the terms:
x2 + -1x2 + 4x2y2 + x4y + y = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 4x2y2 + x4y + y = 0 + -1x2
4x2y2 + x4y + y = 0 + -1x2
Remove the zero:
4x2y2 + x4y + y = -1x2

Add '-4x2y2' to each side of the equation.
4x2y2 + x4y + -4x2y2 + y = -1x2 + -4x2y2

Reorder the terms:
4x2y2 + -4x2y2 + x4y + y = -1x2 + -4x2y2

Combine like terms: 4x2y2 + -4x2y2 = 0
0 + x4y + y = -1x2 + -4x2y2
x4y + y = -1x2 + -4x2y2

Add '-1x4y' to each side of the equation.
x4y + -1x4y + y = -1x2 + -4x2y2 + -1x4y

Combine like terms: x4y + -1x4y = 0
0 + y = -1x2 + -4x2y2 + -1x4y
y = -1x2 + -4x2y2 + -1x4y

Add '-1y' to each side of the equation.
y + -1y = -1x2 + -4x2y2 + -1x4y + -1y

Combine like terms: y + -1y = 0
0 = -1x2 + -4x2y2 + -1x4y + -1y

Simplifying
0 = -1x2 + -4x2y2 + -1x4y + -1y

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:

| 51+x=153 | | 2(n-1)=7n+8 | | -13+4x=-52+13x | | x+112=153 | | 3*2x-2=-18 | | x^2+y^2+z^2=20x-8y+12z-143 | | 22-6x=13-7x | | 51+x+153=x+112 | | y=16-0.05x | | 3*2x-2=18 | | -(x-2)+10=-3(x-2) | | 2*x+3*x=89 | | 5+10x=-4+x | | 3(x-6)=5(x+8) | | 10x+5=12x-11 | | 3a-4b=5bz+c | | 3*x-7+9*x^2-3=100 | | 2x-(4y-3)+5xz= | | 0.35*50= | | 60+11x-1=3+18x | | 5q+3q=25-9 | | -6+11x+5x-7=147 | | x=x*0.29+312000 | | 79x-2+130=13x | | =56t-16t^2 | | -15k+16k-5=22 | | (x+9)+(x+11)= | | 8*3-1+2(6*4)= | | 4x+1=-1 | | (-2+8i)= | | y=-20x+4 | | 8x-16=2x+20 |

Equations solver categories