y'' - y = 0 Second order differential homogeneous equation

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In this video we find the general solution to the second order differential homogeneous equation y" - y = 0 by first finding the characteristic equation which allows allows us to solve for the roots.
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  2. y'' - y = 0
  3. Solve y - y = 0
  4. y - y = 0 differential equation
  5. y - y = 0 second order differential equation
  6. y - y = 0 second order differential homogeneous equation
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Комментарии
Автор

single root general solution is y= C1e(rx)+C2(x)e(rx) ??

allerlom
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it's weird to see people confusing this with the harmonic equation in this comment section lol
like i know this is youtube comments but come on man pay more attention

AS-ipxf
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Thank you for uploading. then how can I calculate such as y' - y = 5?

johminjun
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Solve the differential equation :
y' + y = 1

pankzvlogs
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This video is completely wrong. The roots are different and the answer should be in the form of cos and sin

jiwonyoun
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a real mathematician on quora had written that if u=y' or u=dy/dx
then y''=du/dx
so dx=du/y'' and
dx=dy/u
so this leads to y''=u*du/dy and i get as new equation
y+u*du/dy=0
this integrates to
y^2=-u^2/2+c1 but now i get stuck. can anyone help me or tell me
the link to a solution?

zdrastvutye
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nice bullshit. single root is y(x) = c1e^rx + c2xe^rx

gabrielgoncalves