Solve equation f'(x)-f"(x)+f(x)=e^x-3 if f(x)=x^2+e^x?

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You need to evaluate the first order derivative, hence, you need to differentiate the function with respect to `x` , such that:

`f'(x) = (x^2+e^x)' => f'(x) = 2x + e^x`

You need to evaluate the second order derivative, hence, you need to differentiate the first order derivative with respect to `x` , such that:

`f''(x) = (2x + e^x)' => f''(x) = 2 + e^x`

You need to replace the equations of the first order derivative and the second order derivative in equation you will solve for `x` , such that:

`2x + e^x - 2 - e^x + x^2 + e^x = e^x - 3`

Reducing duplicate terms and re-arranging the powers in descending order yields:

`x^2 + 2x - 2 = -3 => x^2 + 2x + 3 - 2 = 0`

`x^2 + 2x + 1 = 0 => (x + 1)^2 = 0 => x + 1 = 0 => x = -1`

Hence, evaluating the solutions to the given equation, under the given conditions, yields `x = -1.`

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