(y^2)dy=(x^2)dx-3dx

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Solution for (y^2)dy=(x^2)dx-3dx equation: 


Simplifying
(y2) * dy = (x2) * dx + -3dx

Multiply y2 * dy
dy3 = (x2) * dx + -3dx

Multiply x2 * dx
dy3 = dx3 + -3dx

Reorder the terms:
dy3 = -3dx + dx3

Solving
dy3 = -3dx + dx3

Solving for variable 'd'.

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

Add '3dx' to each side of the equation.
3dx + dy3 = -3dx + 3dx + dx3

Combine like terms: -3dx + 3dx = 0
3dx + dy3 = 0 + dx3
3dx + dy3 = dx3

Add '-1dx3' to each side of the equation.
3dx + -1dx3 + dy3 = dx3 + -1dx3

Combine like terms: dx3 + -1dx3 = 0
3dx + -1dx3 + dy3 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(3x + -1x3 + y3) = 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 '(3x + -1x3 + y3)' equal to zero and attempt to solve:

Simplifying
3x + -1x3 + y3 = 0

Solving
3x + -1x3 + y3 = 0

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

Add '-3x' to each side of the equation.
3x + -1x3 + -3x + y3 = 0 + -3x

Reorder the terms:
3x + -3x + -1x3 + y3 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + -1x3 + y3 = 0 + -3x
-1x3 + y3 = 0 + -3x
Remove the zero:
-1x3 + y3 = -3x

Add 'x3' to each side of the equation.
-1x3 + x3 + y3 = -3x + x3

Combine like terms: -1x3 + x3 = 0
0 + y3 = -3x + x3
y3 = -3x + x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = -3x + x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -3x + x3 + -1y3

Simplifying
0 = -3x + x3 + -1y3

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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