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Simplifying u(t + 1) + -1e3tu(t) = 0 Reorder the terms: u(1 + t) + -1e3tu(t) = 0 (1 * u + t * u) + -1e3tu(t) = 0 Reorder the terms: (tu + 1u) + -1e3tu(t) = 0 (tu + 1u) + -1e3tu(t) = 0 Multiply e3tu * t tu + 1u + -1e3t2u = 0 Reorder the terms: -1e3t2u + tu + 1u = 0 Solving -1e3t2u + tu + 1u = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-1tu' to each side of the equation. -1e3t2u + tu + -1tu + 1u = 0 + -1tu Combine like terms: tu + -1tu = 0 -1e3t2u + 0 + 1u = 0 + -1tu -1e3t2u + 1u = 0 + -1tu Remove the zero: -1e3t2u + 1u = -1tu Add '-1u' to each side of the equation. -1e3t2u + 1u + -1u = -1tu + -1u Combine like terms: 1u + -1u = 0 -1e3t2u + 0 = -1tu + -1u -1e3t2u = -1tu + -1u Divide each side by '-1t2u'. e3 = t-1 + t-2 Simplifying e3 = t-1 + t-2 Reorder the terms: e3 = t-2 + t-1 Reorder the terms: e3 + -1t-2 + -1t-1 = t-2 + -1t-2 + t-1 + -1t-1 Combine like terms: t-2 + -1t-2 = 0 e3 + -1t-2 + -1t-1 = 0 + t-1 + -1t-1 e3 + -1t-2 + -1t-1 = t-1 + -1t-1 Combine like terms: t-1 + -1t-1 = 0 e3 + -1t-2 + -1t-1 = 0 Factor out the Greatest Common Factor (GCF), 't-2'. t-2(e3t2 + -1 + -1t) = 0Subproblem 1
Set the factor 't-2' equal to zero and attempt to solve: Simplifying t-2 = 0 Solving t-2 = 0 Move all terms containing e to the left, all other terms to the right. Add '-1t-2' to each side of the equation. t-2 + -1t-2 = 0 + -1t-2 Remove the zero: 0 = -1t-2 Simplifying 0 = -1t-2 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 '(e3t2 + -1 + -1t)' equal to zero and attempt to solve: Simplifying e3t2 + -1 + -1t = 0 Reorder the terms: -1 + e3t2 + -1t = 0 Solving -1 + e3t2 + -1t = 0 Move all terms containing e to the left, all other terms to the right. Add '1' to each side of the equation. -1 + e3t2 + 1 + -1t = 0 + 1 Reorder the terms: -1 + 1 + e3t2 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + e3t2 + -1t = 0 + 1 e3t2 + -1t = 0 + 1 Combine like terms: 0 + 1 = 1 e3t2 + -1t = 1 Add 't' to each side of the equation. e3t2 + -1t + t = 1 + t Combine like terms: -1t + t = 0 e3t2 + 0 = 1 + t e3t2 = 1 + t Divide each side by 't2'. e3 = t-2 + t-1 Simplifying e3 = t-2 + t-1 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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