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Find linearly independent functions that are annihilated by the given differential operator. (Give as many functions as possible. Use x as the independent variable. Enter your answers as a comma-separated list.) D2 − 6D − 55

Respuesta :

mavila18

Answer:

[tex]\{e^{11x},e^{-5x}\}[/tex]

Step-by-step explanation:

We have the differential operator

[tex]D^{2}-6D-55[/tex]

the factors are

[tex](D-11)(D+5)[/tex]

we also know that for any operator of the form (D - α) the function that is annulated by the operator has the form:

[tex](D-\alpha)^{n} --> x^{n-1}e^{\alpha x}[/tex]

in our case we have n=1 and α=11,-5. Hence we have

[tex](D-11) --> e^{11x}\\(D-(-5)) --> e^{-5x}[/tex]

the solutions are

[tex]\{e^{11x},e^{-5x}\}[/tex]

I hope this is useful for you

regards

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