MAT 330 Quiz One Problem Set.pdf - MAT 330 Quiz One...

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Differential Equations with Boundary-Value Problems
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Chapter 4 / Exercise 3
Differential Equations with Boundary-Value Problems
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MAT 330 Quiz One Assignment Instructions: For each problem, be sure to show all steps for arriving at your solution. Work within this document. Use an equation tool as needed and submit everything in one file. 1. Verify that ?(?) = − 1 14 + 12? 14? is a solution of the ordinary differential equation ? = 14? + 1 . Note you do not need to solve the ordinary differential equation. First order O.D.E. ? = − 1 14 + 12? 14? ? = 14? + 1 ? = 14 ∗ 12? 14? ? = 14 (− 1 14 + 12? 14? ) + 1 ? = 168 ? 14? ? = −1 + 14 ∗ 12? 14? + 1 ? = 14 ∗ 12? 14? ? = 168 ? 14? 2. For the below ordinary differential equation, state the order and determine if the equation is linear or nonlinear. Then find the general solution of the ordinary differential equation. Verify your solution. First Order O.D.E. ?? = 2? ? 2 ? ? = 0 Linear P(x) = 2? ? , Q(x) = 0 𝜇(?) = ? ∫ − 2 𝑥 ?? 𝜇(?) = ? −2 ln ? 𝜇 (?) = 1 ? 2 So, ? ( 1 ? 2 ) = ∫ 0 ∗ ( 1 ? 2 ) ?? ? ( 1 ? 2 ) = ? ? = ? 2 ? Verification ?(? 2 ?)′ = 2(? 2 ?) ? (2??) = 2(? 2 ?) 2? 2 ? = 2? 2 ?
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Differential Equations with Boundary-Value Problems
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Chapter 4 / Exercise 3
Differential Equations with Boundary-Value Problems
Zill
Expert Verified

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