sqrt(5+y^2)dx+4(x^2*y+y)dy=0

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Solution for sqrt(5+y^2)dx+4(x^2*y+y)dy=0 equation: 


Simplifying
sqrt(5 + y2) * dx + 4(x2 * y + y) * dy = 0

Reorder the terms for easier multiplication:
qrst * dx(5 + y2) + 4(x2 * y + y) * dy = 0

Multiply qrst * dx
dqrstx(5 + y2) + 4(x2 * y + y) * dy = 0
(5 * dqrstx + y2 * dqrstx) + 4(x2 * y + y) * dy = 0
(5dqrstx + dqrstxy2) + 4(x2 * y + y) * dy = 0

Multiply x2 * y
5dqrstx + dqrstxy2 + 4(x2y + y) * dy = 0

Reorder the terms for easier multiplication:
5dqrstx + dqrstxy2 + 4dy(x2y + y) = 0
5dqrstx + dqrstxy2 + (x2y * 4dy + y * 4dy) = 0
5dqrstx + dqrstxy2 + (4dx2y2 + 4dy2) = 0

Solving
5dqrstx + dqrstxy2 + 4dx2y2 + 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), 'd'.
d(5qrstx + qrstxy2 + 4x2y2 + 4y2) = 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 '(5qrstx + qrstxy2 + 4x2y2 + 4y2)' equal to zero and attempt to solve:

Simplifying
5qrstx + qrstxy2 + 4x2y2 + 4y2 = 0

Solving
5qrstx + qrstxy2 + 4x2y2 + 4y2 = 0

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

Add '-5qrstx' to each side of the equation.
5qrstx + qrstxy2 + 4x2y2 + -5qrstx + 4y2 = 0 + -5qrstx

Reorder the terms:
5qrstx + -5qrstx + qrstxy2 + 4x2y2 + 4y2 = 0 + -5qrstx

Combine like terms: 5qrstx + -5qrstx = 0
0 + qrstxy2 + 4x2y2 + 4y2 = 0 + -5qrstx
qrstxy2 + 4x2y2 + 4y2 = 0 + -5qrstx
Remove the zero:
qrstxy2 + 4x2y2 + 4y2 = -5qrstx

Add '-1qrstxy2' to each side of the equation.
qrstxy2 + 4x2y2 + -1qrstxy2 + 4y2 = -5qrstx + -1qrstxy2

Reorder the terms:
qrstxy2 + -1qrstxy2 + 4x2y2 + 4y2 = -5qrstx + -1qrstxy2

Combine like terms: qrstxy2 + -1qrstxy2 = 0
0 + 4x2y2 + 4y2 = -5qrstx + -1qrstxy2
4x2y2 + 4y2 = -5qrstx + -1qrstxy2

Add '-4x2y2' to each side of the equation.
4x2y2 + -4x2y2 + 4y2 = -5qrstx + -1qrstxy2 + -4x2y2

Combine like terms: 4x2y2 + -4x2y2 = 0
0 + 4y2 = -5qrstx + -1qrstxy2 + -4x2y2
4y2 = -5qrstx + -1qrstxy2 + -4x2y2

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -5qrstx + -1qrstxy2 + -4x2y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -5qrstx + -1qrstxy2 + -4x2y2 + -4y2

Simplifying
0 = -5qrstx + -1qrstxy2 + -4x2y2 + -4y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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