the solution of (12x+5y-9)dx+(5x+2y-4)dy=0 is
Answers
Answer:
Simplifying (12x + 5y + -9) * dx + (5x + 2y + -3) * dy = 0 Reorder the terms: (-9 + 12x + 5y) * dx + (5x + 2y + -3) * dy = 0 Reorder the terms for easier multiplication: dx(-9 + 12x + 5y) + (5x + 2y + -3) * dy = 0 (-9 * dx + 12x * dx + 5y * dx) + (5x + 2y + -3) * dy = 0 Reorder the terms: (-9dx + 5dxy + 12dx2) + (5x + 2y + -3) * dy = 0 (-9dx + 5dxy + 12dx2) + (5x + 2y + -3) * dy = 0 Reorder the terms: -9dx + 5dxy + 12dx2 + (-3 + 5x + 2y) * dy = 0 Reorder the terms for easier multiplication: -9dx + 5dxy + 12dx2 + dy(-3 + 5x + 2y) = 0 -9dx + 5dxy + 12dx2 + (-3 * dy + 5x * dy + 2y * dy) = 0 Reorder the terms: -9dx + 5dxy + 12dx2 + (5dxy + -3dy + 2dy2) = 0 -9dx + 5dxy + 12dx2 + (5dxy + -3dy + 2dy2) = 0 Reorder the terms: -9dx + 5dxy + 5dxy + 12dx2 + -3dy + 2dy2 = 0 Combine like terms: 5dxy + 5dxy = 10dxy -9dx + 10dxy + 12dx2 + -3dy + 2dy2 = 0 Solving -9dx + 10dxy + 12dx2 + -3dy + 2dy2 = 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(-9x + 10xy + 12x2 + -3y + 2y2) = 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 '(-9x + 10xy + 12x2 + -3y + 2y2)' equal to zero and attempt to solve: Simplifying -9x + 10xy + 12x2 + -3y + 2y2 = 0 Solving -9x + 10xy + 12x2 + -3y + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '9x' to each side of the equation. -9x + 10xy + 12x2 + -3y + 9x + 2y2 = 0 + 9x Reorder the terms: -9x + 9x + 10xy + 12x2 + -3y + 2y2 = 0 + 9x Combine like terms: -9x + 9x = 0 0 + 10xy + 12x2 + -3y + 2y2 = 0 + 9x 10xy + 12x2 + -3y + 2y2 = 0 + 9x Remove the zero: 10xy + 12x2 + -3y + 2y2 = 9x Add '-10xy' to each side of the equation. 10xy + 12x2 + -3y + -10xy + 2y2 = 9x + -10xy Reorder the terms: 10xy + -10xy + 12x2 + -3y + 2y2 = 9x + -10xy Combine like terms: 10xy + -10xy = 0 0 + 12x2 + -3y + 2y2 = 9x + -10xy 12x2 + -3y + 2y2 = 9x + -10xy Add '-12x2' to each side of the equation. 12x2 + -3y + -12x2 + 2y2 = 9x + -10xy + -12x2 Reorder the terms: 12x2 + -12x2 + -3y + 2y2 = 9x + -10xy + -12x2 Combine like terms: 12x2 + -12x2 = 0 0 + -3y + 2y2 = 9x + -10xy + -12x2 -3y + 2y2 = 9x + -10xy + -12x2 Add '3y' to each side of the equation. -3y + 3y + 2y2 = 9x + -10xy + -12x2 + 3y Combine like terms: -3y + 3y = 0 0 + 2y2 = 9x + -10xy + -12x2 + 3y 2y2 = 9x + -10xy + -12x2 + 3y Add '-2y2' to each side of the equation. 2y2 + -2y2 = 9x + -10xy + -12x2 + 3y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = 9x + -10xy + -12x2 + 3y + -2y2 Simplifying 0 = 9x + -10xy + -12x2 + 3y + -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}
evaluate (12x+5y-9)dx+ (5x-2y-4)dy=0