These two questions are related; I went through the first question and they all seem like regular separable equations, what am I missing? 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) \( \frac{dy}{dx} - \frac{2}{x}y = 0 \)(b) \( x^2\frac{dy}{dx} + 2xy = 0 \)(c) \( y^2 - xy\frac{dy}{dx} = 0 \)(d) \( xy^3 + \frac{1}{x}y + \frac{dy}{dx} = 0 \)(e) \( \frac{dy}{dx} = (x + y + 2)^2 \)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.

(1) (a) Given differential equation dydx−2xy=0. Hence, it is separable. It is linear in y. The…

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) - žy = 0 (b) x2 + 2xy = 0 dx (c) y² – xy = 0 (d) æy³ + ¿y + = 0 (e) = (x+ y+2)²

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) - žy = 0 (b) x2 + 2xy = 0 dx (c) y² – xy = 0 (d) æy³ + ¿y + = 0 (e) = (x+ y+2)²

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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Question

These two questions are related; I went through the first question and they all seem like regular separable equations, what am I missing?

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) \( \frac{dy}{dx} - \frac{2}{x}y = 0 \)

(b) \( x^2\frac{dy}{dx} + 2xy = 0 \)

(c) \( y^2 - xy\frac{dy}{dx} = 0 \)

(d) \( xy^3 + \frac{1}{x}y + \frac{dy}{dx} = 0 \)

(e) \( \frac{dy}{dx} = (x + y + 2)^2 \)

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.

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