A calibration curve y(x) of a sensor satisfies y'' + y' - 6y = 0…

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A calibration curve $y(x)$ of a sensor satisfies $y'' + y' - 6y = 0$ . Its general solution is $y = Ae^{2x} + Be^{-3x}$ . The curve starts at $y(0) = 7$ with the slope $y'(0) = -1$ . Find the constants $A$ and $B$ , and then the value $y(1)$ to four decimal places.

Need a reminder? The key ideaShow

The order is the order of the highest derivative. The degree is its power, once roots and fractions of derivatives are cleared. A general solution has as many constants as the order, and conditions fix them.

\displaystyle \text{order } n \ \Rightarrow\ n \text{ constants}.

The worked solution

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A calibration curve y(x) of a sensor satisfies y'' + y' - 6y = 0…

The worked solution

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