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  3. consider the following 2nd order linear constant coefficient homogenous ordinary...

Question: consider the following 2nd order linear constant coefficient homogenous ordinary...

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Consider the following 2nd order, linear, constant coefficient, homogenous, ordinary differential equation (ODE) that describes how some parameter θ varies with the independent variable x. Note m is a constant. d2e dx2 a. How many initial and boundary conditions are required to find a particular solution? b. Prove that the general solution is given by C1eC2ex c If a boundary condition requires that 60 as xinfinity, how does the general solution simplify? d. Sketch vs. x for x>0 under the condition in part c. e. Compute the average value of θ within a domain 0 < x < L under the condition in part c d2e f. Consider a non-homogenous form of the ODE above given by where both m and b are constants. Determine the general solution and show it satisfies the differential equation. hint the constant b needs to be incorporated into the given homogenous solution)

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