Differential Equations - 22 - Why superimpose? (y=c1y1+c2y2)

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Answering a question that was submitted to me: why do we take our solution to be linear combinations of the two solutions associated with our two roots?!
  1. The Lazy Engineer
  2. Differential Equations
  3. Diff eq
  4. 2nd
  5. second
  6. order
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Differential Equations - 22 - Why superimpose? (y=c1y1+c2y2)

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Комментарии
Автор

This right here is crazy lol I think it's starting to make sense. Because it's linear, it's actually just like taking the differential equation evaluated at y1, and adding that to the differential equation evaluated at y2. Since each is a solution, each differential equation itself is 0 = 0, and so that equation plus itself is still 0 = 0 and is still totally a solution/valid. Wow!

uselessdiscussion
Автор

Thank you for your great videos

I have question : if we look at it geometrically then Y1 and Y2 and Y=Y1+Y2 are three different functions that satifies our differential equation, so we will draw three different functions that are totally different when C1 and C2 are non zero . Accordingly how Y includes Y1 and Y2 knowing that graphically they are totally different functions ?

Thank you

mohfa
Автор

What if one solution is zero, then do we need to write it as y= c1 + c2e

senurahansaja
Автор

To be able to put two intial conditions

Ahmad-gnpd