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(d) Summarize the method used for solving homogeneous equations. Identify one equation in (1) that is homogeneous and solve it. (e) Summarize the method used for solving Bernoulli equations. Identify one equation in (1) that is homogeneous and solve it.

(d) Summarize the method used for solving homogeneous equations. Identify one equation in (1) that is homogeneous and solve it. (e) Summarize the method used for solving Bernoulli equations. Identify one equation in (1) that is homogeneous and solve it.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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for question 2 part d-e

1. For each first order ODE, determine if it is separable, linear, exact or exact after using an integrating factor, homogeneous, and/or Bernoulli. Multiple labels may apply. Justify all conclusions. You do not need to solve. (a) - ²y = 0 (b) x² + 2xy = 0 (c) y² - xy = 0 (d) ry³ + ¹y+d=0 (e) = (x+y + 2)²
Transcribed Image Text:1. For each first order ODE, determine if it is separable, linear, exact or exact after using an integrating factor, homogeneous, and/or Bernoulli. Multiple labels may apply. Justify all conclusions. You do not need to solve. (a) - ²y = 0 (b) x² + 2xy = 0 (c) y² - xy = 0 (d) ry³ + ¹y+d=0 (e) = (x+y + 2)²
2. (a) What theorem is used to justify the method of solving separable equations? Identify one of the equations in (1) that is separable and solve it. (b) Summarize the method used for solving linear, first-order ODE's. What theorem is used to justify this method? Identify one of the equations in (1) that is linear and solve it. (c) Summarize the idea behind exact ODE's. Identify one equation in (1) that is either exact or exact after using an integrating factor and solve it. (d) Summarize the method used for solving homogeneous equations. Identify one equation in (1) that is homogeneous and solve it. (e) Summarize the method used for solving Bernoulli equations. Identify one equation in (1) that is homogeneous and solve it.
Transcribed Image Text:2. (a) What theorem is used to justify the method of solving separable equations? Identify one of the equations in (1) that is separable and solve it. (b) Summarize the method used for solving linear, first-order ODE's. What theorem is used to justify this method? Identify one of the equations in (1) that is linear and solve it. (c) Summarize the idea behind exact ODE's. Identify one equation in (1) that is either exact or exact after using an integrating factor and solve it. (d) Summarize the method used for solving homogeneous equations. Identify one equation in (1) that is homogeneous and solve it. (e) Summarize the method used for solving Bernoulli equations. Identify one equation in (1) that is homogeneous and solve it.
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