Mathematics

Mathematics

Problem

For the differential equation dydx=y\dfrac{dy}{dx}=y with initial condition y(0)=1y(0)=1, three equal straight-line steps of length 0.10.1 are taken to approximate y(0.3)y(0.3). The approximate value obtained is 1.3311.331. The exact value is e0.3≈1.3499e^{0.3}\approx1.3499. Calculate the percentage error of the approximation, to the nearest hundredth of a percent.

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