can soneone help me with question 123SolutionSimplifying 2x2

can soneone help me with question 123?

Solution

Simplifying

(2x² + y) * dx + (x²y + -1x) * dy = 0

Reorder the terms for easier multiplication:

dx(2x² + y) + (x²y + -1x) * dy = 0

(2x² * dx + y * dx) + (x²y + -1x) * dy = 0

Reorder the terms:

(dxy + 2dx³) + (x²y + -1x) * dy = 0

(dxy + 2dx³) + (x²y + -1x) * dy = 0

Reorder the terms:

dxy + 2dx³ + (-1x + x²y) * dy = 0

Reorder the terms for easier multiplication:

dxy + 2dx³ + dy(-1x + x²y) = 0

dxy + 2dx³ + (-1x * dy + x²y * dy) = 0

dxy + 2dx³ + (-1dxy + dx²y²) = 0

Reorder the terms:

dxy + -1dxy + dx²y² + 2dx³ = 0

Combine like terms: dxy + -1dxy = 0

0 + dx²y² + 2dx³ = 0

dx²y² + 2dx³ = 0

Solving

dx²y² + 2dx³ = 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), \'dx²\'.

dx²(y² + 2x) = 0

Subproblem 1

Set the factor \'dx²\' equal to zero and attempt to solve:

Simplifying

dx² = 0

Solving

dx² = 0

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

Simplifying

dx² = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor \'(y² + 2x)\' equal to zero and attempt to solve:

Simplifying

y² + 2x = 0

Reorder the terms:

2x + y² = 0

Solving

2x + y² = 0

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

Add \'-2x\' to each side of the equation.

2x + -2x + y² = 0 + -2x

Combine like terms: 2x + -2x = 0

0 + y² = 0 + -2x

y² = 0 + -2x

Remove the zero:

y² = -2x

Add \'-1y²\' to each side of the equation.

y² + -1y² = -2x + -1y²

Combine like terms: y² + -1y² = 0

0 = -2x + -1y²

Simplifying

0 = -2x + -1y²