4. Consider the differential equation: y'+y+x 0 (a) Is the differential equation separable? If yes, write it in the form y' = f(x)g(y). (b) Is the differential equation linear? If yes, write it in standard form. (c) Is the differential equation Bernoulli? If yes, write it in the form y' + p(x)y = q(x)y" (d) Is the differential equation homogeneous? If yes, write it in the form y' = F (2). (e) Solve the differential equation using one of them methods you have identified in (a)-(d).

4. Consider the differential equation: y'+y+x 0 (a) Is the differential equation separable? If yes, write it in the form y' = f(x)g(y). (b) Is the differential equation linear? If yes, write it in standard form. (c) Is the differential equation Bernoulli? If yes, write it in the form y' + p(x)y = q(x)y" (d) Is the differential equation homogeneous? If yes, write it in the form y' = F (2). (e) Solve the differential equation using one of them methods you have identified in (a)-(d).

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

4. Consider the differential equation:
xy' + y + x = 0
(a) Is the differential equation separable? If yes, write it in the form y' =
f(x)g(y).
(b) Is the differential equation linear? If yes, write it in standard form.
(c) Is the differential equation Bernoulli? If yes, write it in the form y' + p(x)y = q(x)y"
(d) Is the differential equation homogeneous? If yes, write it in the form y' = F (!).
(e) Solve the differential equation using one of them methods you have identified in (a)-(d).
5. Self-Reflection: We have now learned several methods for solving first-order ODES.
paragraphs reflecting on how confident you do/don't feel in your ability to solve a differential equation
using each of the methods? Are there any methods that you would like to practice more? Do you
have any questions that you want/need to ask about first-order differential equations?
Write 1-2

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