Linear systems diff eq question

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SUMMARY

The discussion centers on solving the linear differential equation y' + 4y = δ(x), where δ(x) represents the Dirac delta function. Participants confirm the equation's structure and discuss the assumption of an initial condition, typically y(0-) = 0, which is common in engineering contexts. The conversation highlights the importance of clarity in problem statements and the need for foundational knowledge in differential equations to navigate such queries effectively.

PREREQUISITES
  • Understanding of linear differential equations
  • Familiarity with the Dirac delta function
  • Knowledge of initial conditions in differential equations
  • Basic skills in mathematical problem-solving
NEXT STEPS
  • Study the properties and applications of the Dirac delta function
  • Learn techniques for solving linear differential equations
  • Explore initial value problems in differential equations
  • Review resources on differential equations, such as "Elementary Differential Equations" by William E. Boyce
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Students and professionals in engineering, mathematics, and physics who are dealing with linear differential equations and their applications in various fields.

sdusheyko
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given x(t)=impulse
find y(t)

y(prime)=4y=8x

i am lost
 
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I assume there's a typo in your post and the differential equation is actually y'+4y=8x, so you want to solve

y'+4y=\delta(x)

where \delta(x) is the Dirac delta function. Is this right? Did the problem specify an initial condition? (Engineers typically assume y(0-)=0.)
 
vela said:
I assume there's a typo in your post and the differential equation is actually y'+4y=8x, so you want to solve

y'+4y=\delta(x)

where \delta(x) is the Dirac delta function. Is this right? Did the problem specify an initial condition? (Engineers typically assume y(0-)=0.)

you're right about everything you've said. I'm going to stick my head in a diff eq book and if i get lost i'll probably come back and whine.

thanks
 

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