Thursday, August 14, 2014

`y = cosx` Determine whether the function is a solution of the differential equation `xy' - 2y = x^3e^x`

To check whether the given function is a solution of the given equation, we first need to calculate the derivative of the function.


`y'=-sin x` 


Now we substitute that into the equation.


`-x sin x-2cos x ne x^3e^x`  


Obviously, the two sides of the equation are not equal, hence the given function is not a solution of the differential equation.                           

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