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t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a \"Cauchy-Euler equation.\"...

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Physics

t2 (d2r/dt2) - 9t (dr/dt) + 16r= 4 is an example of a \"Cauchy-Euler equation.\" Such equationsappear in a number of physics and engineering applications.

a) Write the complementary homogeneous equation.

b) Plug r = ekt into the equation you wrote in parta. Show that this solution will not work for any constant k: thisequation has no exponential solution.

c) Plug the guess r = tn (where n is a constant) intothe equation you wrote for part a. Solve the resulting algebraicequation for n; you should find 2 solutions.

d) Write the general solution to the equation you wrote in Parta.

e) Find a specific solution to the origianl (inhomogeneous)equation.

f) Write the general solution to the inhomogeneous equation.

g) What is it about this particular equation that made r =tn work?

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