2nd order nonhomogeneos differential equations with initial conditions

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Discussion Overview

The discussion revolves around solving a second-order non-homogeneous differential equation with initial conditions. The equation presented involves imaginary roots and requires finding both the homogeneous and particular solutions.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the differential equation d^2y/dt^2 + 15y = cos 4t + 2 sin t and describes the process of finding the homogeneous solution, noting the imaginary roots.
  • Another participant suggests using initial conditions to solve for constants C1 and C2 in the homogeneous solution.
  • A participant expresses uncertainty about how to find the particular solution for the inhomogeneous part of the equation.
  • One participant comments that the thread should be posted in the Homework & Coursework section, indicating a concern about the appropriateness of the discussion's location.

Areas of Agreement / Disagreement

There is no consensus on how to proceed with finding the particular solution, and the discussion remains unresolved regarding the next steps in solving the differential equation.

Contextual Notes

Participants have not provided the initial conditions necessary for solving for C1 and C2, and there is a lack of clarity on how to set up the particular solution for the non-homogeneous part of the equation.

pedro123
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I have a problem which in involves a second order differential equations with imaginary roots and I can seem to know how to finish the problem.

d^2y/dt^2 +15y =cos 4t+2 sin t

this is what I got so far


r^2+15=0 for the homogeneous part

r=+-(√15)

Yh=C1cos√15+C2sin√15

now is where I get stuck
 
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You've got to use the initial conditions to solve for C1 and C2 in order to complete the homogeneous solution. Then, you get to find the particular solution for in inhomogeneous equation.
 
yes I know but can you explain how

i know i need to have a particular solution for cos 4t+2 sin t
but i don't know how to set up
 
Problems such as these should be posted in the Homework & Coursework section, not in the technical math sections. I am closing this thread.
 

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