To construct each IVP, choose a pair of scalars X and (if complex, and...
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To construct each IVP, choose a pair of scalars X₁ and ₂ (if complex, ₁ and λ2 must be complex conjugate) • an invertible matrix Uthat is not the identity matrix • an initial value xo. If X₁ and ₂ are real, set P=U | 2]U-¹. If λ₁ = a + ßiand A₂ = a - Bifor some real numbers a and B, set 0 α P=U [° -2]U-¹. α Solve the IVP x' = Px and x(0) = x₁ two different ways: i. Apply the "IKEA method" described in Friday's lecture, using the information that you already know because you used it to construct P. ii. Apply the relevant method described in Notes on Diffy Q's to find the general solution, then solve for the constants C₁ and c₂ to find the solution of the IVP. Verify that you obtain the same answer from both approaches. Problems Create and solve four IVPs, following the instructions given above, one for each of the following situations: 1. Distinct real nonzero ₁ and 2 2. λ₁ = 0 + A₂ 3. A₁ = Biand A₂ = - Bi for real B 4. A₁ = a + ßiand A₂ = a - Bifor nonzero real numbers a and B, To construct each IVP, choose a pair of scalars X₁ and ₂ (if complex, ₁ and λ2 must be complex conjugate) • an invertible matrix Uthat is not the identity matrix • an initial value xo. If X₁ and ₂ are real, set P=U | 2]U-¹. If λ₁ = a + ßiand A₂ = a - Bifor some real numbers a and B, set 0 α P=U [° -2]U-¹. α Solve the IVP x' = Px and x(0) = x₁ two different ways: i. Apply the "IKEA method" described in Friday's lecture, using the information that you already know because you used it to construct P. ii. Apply the relevant method described in Notes on Diffy Q's to find the general solution, then solve for the constants C₁ and c₂ to find the solution of the IVP. Verify that you obtain the same answer from both approaches. Problems Create and solve four IVPs, following the instructions given above, one for each of the following situations: 1. Distinct real nonzero ₁ and 2 2. λ₁ = 0 + A₂ 3. A₁ = Biand A₂ = - Bi for real B 4. A₁ = a + ßiand A₂ = a - Bifor nonzero real numbers a and B,
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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