Graph the line that passes through the two points. (0,0) , (1/3,7/3)
1 answer:
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Answer:
x'-5x=0, or x''-25x=0, or x'''-125x=0
Step-by-step explanation:
The function is infinitely differentiable, so it satisfies a infinite number of differential equations. The required answer depends on your previous part, so I will describe a general procedure to obtain the equations.
Using rules of differentiation, we obtain that . Differentiate again to obtain,
. Repeating this process,
.
This can repeated infinitely, so it is possible to obtain a differential equation of order n. The key is to differentiate the required number of times and write the equation in terms of x.