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Simplifying (1 + 2y2) * dy = ycosdx Reorder the terms for easier multiplication: dy(1 + 2y2) = ycosdx (1 * dy + 2y2 * dy) = ycosdx (1dy + 2dy3) = ycosdx Solving 1dy + 2dy3 = cdosxy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1cdosxy' to each side of the equation. 1dy + -1cdosxy + 2dy3 = cdosxy + -1cdosxy Reorder the terms: -1cdosxy + 1dy + 2dy3 = cdosxy + -1cdosxy Combine like terms: cdosxy + -1cdosxy = 0 -1cdosxy + 1dy + 2dy3 = 0 Factor out the Greatest Common Factor (GCF), 'dy'. dy(-1cosx + 1 + 2y2) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(-1cosx + 1 + 2y2)' equal to zero and attempt to solve: Simplifying -1cosx + 1 + 2y2 = 0 Reorder the terms: 1 + -1cosx + 2y2 = 0 Solving 1 + -1cosx + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1cosx + -1 + 2y2 = 0 + -1 Reorder the terms: 1 + -1 + -1cosx + 2y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1cosx + 2y2 = 0 + -1 -1cosx + 2y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1cosx + 2y2 = -1 Add 'cosx' to each side of the equation. -1cosx + cosx + 2y2 = -1 + cosx Combine like terms: -1cosx + cosx = 0 0 + 2y2 = -1 + cosx 2y2 = -1 + cosx Add '-2y2' to each side of the equation. 2y2 + -2y2 = -1 + cosx + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -1 + cosx + -2y2 Simplifying 0 = -1 + cosx + -2y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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