Sanjay K.
asked • 09/19/19prove that the function,1 x, x^ linear independence has from the differential equation whose roots are 1, x,x^.
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Patrick B. answered • 01/20/20
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characteristic polynomial must be (x-1)^k which has solution x=1 with multiplicity k.
So the solution of the differential equation is 1,x,x^2, x^3, ..., x^k
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Mark H.
This is slightly different from your previous version, but still does not make sense. e.g. what is " x^"? And did you mean to say: "....function.....has linear independence from...."? A function definition needs to be something like y = f(x) = x^2 + 3x + 1 (i.e. a dependent variable set equal to an expression using the independent variable.)09/19/19