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Simplifying (6x3y + cosy) * dx + (9x2y2 + -1xsiny) * dy = 0 Reorder the terms: (cosy + 6x3y) * dx + (9x2y2 + -1xsiny) * dy = 0 Reorder the terms for easier multiplication: dx(cosy + 6x3y) + (9x2y2 + -1xsiny) * dy = 0 (cosy * dx + 6x3y * dx) + (9x2y2 + -1xsiny) * dy = 0 (cdosxy + 6dx4y) + (9x2y2 + -1xsiny) * dy = 0 Reorder the terms: cdosxy + 6dx4y + (-1insxy + 9x2y2) * dy = 0 Reorder the terms for easier multiplication: cdosxy + 6dx4y + dy(-1insxy + 9x2y2) = 0 cdosxy + 6dx4y + (-1insxy * dy + 9x2y2 * dy) = 0 cdosxy + 6dx4y + (-1dinsxy2 + 9dx2y3) = 0 Reorder the terms: cdosxy + -1dinsxy2 + 9dx2y3 + 6dx4y = 0 Solving cdosxy + -1dinsxy2 + 9dx2y3 + 6dx4y = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add 'dinsxy2' to each side of the equation. cdosxy + -1dinsxy2 + 9dx2y3 + dinsxy2 + 6dx4y = 0 + dinsxy2 Reorder the terms: cdosxy + -1dinsxy2 + dinsxy2 + 9dx2y3 + 6dx4y = 0 + dinsxy2 Combine like terms: -1dinsxy2 + dinsxy2 = 0 cdosxy + 0 + 9dx2y3 + 6dx4y = 0 + dinsxy2 cdosxy + 9dx2y3 + 6dx4y = 0 + dinsxy2 Remove the zero: cdosxy + 9dx2y3 + 6dx4y = dinsxy2 Add '-9dx2y3' to each side of the equation. cdosxy + 9dx2y3 + -9dx2y3 + 6dx4y = dinsxy2 + -9dx2y3 Combine like terms: 9dx2y3 + -9dx2y3 = 0 cdosxy + 0 + 6dx4y = dinsxy2 + -9dx2y3 cdosxy + 6dx4y = dinsxy2 + -9dx2y3 Add '-6dx4y' to each side of the equation. cdosxy + 6dx4y + -6dx4y = dinsxy2 + -9dx2y3 + -6dx4y Combine like terms: 6dx4y + -6dx4y = 0 cdosxy + 0 = dinsxy2 + -9dx2y3 + -6dx4y cdosxy = dinsxy2 + -9dx2y3 + -6dx4y Divide each side by 'dosxy'. c = ino-1y + -9o-1s-1xy2 + -6o-1s-1x3 Simplifying c = ino-1y + -9o-1s-1xy2 + -6o-1s-1x3
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