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anonymous

  • 4 years ago

Suppose that y1(t) and y2(t) are both solutions to the differential equation dy/dt= a(t)y + b(t). Write down a linear differential equation satisfied by y1(t) + y2(t).

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  1. bahrom7893
    • 4 years ago
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    crap i forgot how to do this lol.. hold on... let's roll those marbles around

  2. bahrom7893
    • 4 years ago
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    Turing do u remember how to do this?

  3. TuringTest
    • 4 years ago
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    I'm not sure if you need to actually solve it or not...

  4. bahrom7893
    • 4 years ago
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    No you don't.. I don't think so.. It's like this form with the constant

  5. JamesJ
    • 4 years ago
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    If y1 and y2 are solutions to that above equation, then for each of them y' - a(t)y = b(t) Hence y1' - a(t)y1 = b(t) y2' - a(t)y2 = b(t) Add these equations together and you'll see what is the linear INhomogeneous equation satisfied by y1 + y2

  6. bahrom7893
    • 4 years ago
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    OHHHHH JamesJ tnx lol

  7. JamesJ
    • 4 years ago
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    I guess the point of this exercise is to show you that the sum of solutions to an inhomogeneous equation cannot be added together, as would be the case with solutions to a homogeneous equation.

  8. TuringTest
    • 4 years ago
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    ahhh...

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