Differential Equation

Question

a) Let y‴−10y″+21y′=0. 

Find all values of r such that y=erx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list. 

b) Let y″−4y=0. 

Find all values of r such that y=erx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list. 

Answer 1

(a) try y = Ce^rx Every time you take a derivative you bring out an r so that y' = ry, y''=r²y and y''' = r³y

You get the characteristic equation r³-10r²+21 = 0 which can be factored to r(r-3)(r-7) so the roots are 0,3,and 7

I'll leave (b) to you.

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