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provide full handwritten solution Consider the differential equation - - 2x, with initial condition y(0) = 7. (1) Verify by direct substitution that y(x) =

provide full handwritten solution

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Consider the differential equation - - 2x, with initial condition y(0) = 7. (1) Verify by direct substitution that y(x) = 21- 2 + 7 is the solution of the differential equation above with the given initial condition. (2) Use Euler's method with two steps to estimate y when x - 1: y(1) |. What is the magnitude of the error? Error = (3) Use Euler's method with four steps to estimate y when x - 1:y(1) ~ What is the magnitude of the error? Error = (4) By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)? factor

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