Question

Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.

Answer 1

Answer:

  see below for the tables

Step-by-step explanation:

The differential equation is separable, so the solution is ...

  $\displaystyle\dfrac{dy}{dx}=2xy\\\\\int{\dfrac{dy}{y}}=\int{2x}\,dx\\\\\ln{y}=x^2+C\\\\\text{Considering the initial condition, C=-1 }\\\\\boxed{y=e^{x^2-1}}$

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The values for yn are y+y'·h = y+2xyh. We take the "absolute error" to be the (signed) difference between the calculated yn and the actual value y(x).