Monday, July 18, 2011

Determine whether the function is a solution of the differential equation

First, determine the derivative of the given function:    Then substitute and into the given equation:



Is this a true equality for all x? No. To prove this, divide by



We know that is a bounded function (it is obviously by the absolute value if ), and is also bounded, but tends to infinity when  Therefore this equality is false for all x's large enough.

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