Answer each question as a discussion form with 25 to 50 words:
Make up a differential equation that you feel confident possesses only the trivial solution y = 0. Explain your reasoning.
What is missing here; can I specify y(0)=0? Because if I can, then the differential equation dy/dx = ex – x for y(0) = 0 possesses only the trivial solution since it is the derivative of the equation y(x)=ex – 1
For a function to have only a trivial solution of zero, I think we need a function that is zero everywhere which we can then take the derivative of.
Answer each question as a discussion form with 25 to 50 words:
Make up a differential equation that you feel confident possesses only the trivial solution y = 0. Explain your reasoning.
What is missing here; can I specify y(0)=0? Because if I can, then the differential equation dy/dx = ex – x for y(0) = 0 possesses only the trivial solution since it is the derivative of the equation y(x)=ex – 1
For a function to have only a trivial solution of zero, I think we need a function that is zero everywhere which we can then take the derivative of. If am not mistaken, Sin y – sin (pi – y) = 0 for any value of y. The derivative of this function is cos y – cos (pi- y) which is zero too. Is that correct?
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