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Math Help - Acceleration and Ode's

  1. #1
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    Acceleration and Ode's

    ok this prob is a little trickier (x double dot) is given. in gen as a func of x, x dot and t, and here by expression -dot of x + 2e^(-t)+1

    Find solution for x(t)
    which satisfies x(0)= dot of x(0)=0

    I can do init conditions ok on this I think, I'd just like to see how the process of the equation works on this, its probz done in a similar way to the previous one...
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  2. #2
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    Quote Originally Posted by reivera View Post
    ok this prob is a little trickier (x double dot) is given. in gen as a func of x, x dot and t, and here by expression -dot of x + 2e^(-t)+1

    Find solution for x(t)
    which satisfies x(0)= dot of x(0)=0

    I can do init conditions ok on this I think, I'd just like to see how the process of the equation works on this, its probz done in a similar way to the previous one...
    Substitute v = \frac{dx}{dt} and solve the first order DE

    \frac{dv}{dt} = -v + 2 e^{-t} + 1 \Rightarrow \frac{dv}{dt} + v = 2 e^{-t} + 1 \, subject to the initial condition v(0) = 0. I recommend the integrating factor technique.

    Then solve the first order DE

    \frac{dx}{dt} = v(t)\, subject to the initial condition x(0) = 0.
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