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Simplifying (D2 + 3D + -5) * y = e2x + 3x2 + 4x + -1 Reorder the terms: (-5 + 3D + D2) * y = e2x + 3x2 + 4x + -1 Reorder the terms for easier multiplication: y(-5 + 3D + D2) = e2x + 3x2 + 4x + -1 (-5 * y + 3D * y + D2 * y) = e2x + 3x2 + 4x + -1 (-5y + 3yD + yD2) = e2x + 3x2 + 4x + -1 Reorder the terms: -5y + 3yD + yD2 = -1 + e2x + 4x + 3x2 Solving -5y + 3yD + yD2 = -1 + e2x + 4x + 3x2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Reorder the terms: 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = -1 + e2x + 4x + 3x2 + 1 + -1e2x + -4x + -3x2 Reorder the terms: 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = -1 + 1 + e2x + -1e2x + 4x + -4x + 3x2 + -3x2 Combine like terms: -1 + 1 = 0 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = 0 + e2x + -1e2x + 4x + -4x + 3x2 + -3x2 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = e2x + -1e2x + 4x + -4x + 3x2 + -3x2 Combine like terms: e2x + -1e2x = 0 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = 0 + 4x + -4x + 3x2 + -3x2 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = 0 + 3x2 + -3x2 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 1 + -1e2x + -4x + -3x2 + -5y + 3yD + yD2 = 0 The solution to this equation could not be determined.
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