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Simplifying xdy + -1ydx = (1 + y2) * dy Combine like terms: dxy + -1dxy = 0 0 = (1 + y2) * dy Reorder the terms for easier multiplication: 0 = dy(1 + y2) 0 = (1 * dy + y2 * dy) 0 = (1dy + dy3) Solving 0 = 1dy + dy3 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dy' to each side of the equation. 0 + -1dy = 1dy + -1dy + dy3 Remove the zero: -1dy = 1dy + -1dy + dy3 Combine like terms: 1dy + -1dy = 0 -1dy = 0 + dy3 -1dy = dy3 Add '-1dy3' to each side of the equation. -1dy + -1dy3 = dy3 + -1dy3 Combine like terms: dy3 + -1dy3 = 0 -1dy + -1dy3 = 0 Factor out the Greatest Common Factor (GCF), '-1dy'. -1dy(1 + y2) = 0 Ignore the factor -1.Subproblem 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 '(1 + y2)' equal to zero and attempt to solve: Simplifying 1 + y2 = 0 Solving 1 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 0 + -1 y2 = 0 + -1 Combine like terms: 0 + -1 = -1 y2 = -1 Add '-1y2' to each side of the equation. y2 + -1y2 = -1 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1 + -1y2 Simplifying 0 = -1 + -1y2 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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