# 6. a. For the differential equation y ‘ = y , find the solution satisfying y (0) =1. b. Then use…

6. a. For the differential equation *y*' = *y*, find the solution satisfying

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6. a. For the differential equation y ‘ = y , find the solution satisfying y (0) =1. b. Then use…

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*y*(0) =1.

b. Then use Euler’s method with a step size of 0.1 to approximate the value of *y*(1).

c. Then recompute using step sizes of 0.05 and 0.01. How do these compare to the approximation above with step size 0.1?

d. Using the value of *e *as approximately 2.718281, how does the error change as we vary the step size?

7. Use Euler’s method to approximate the solution of the differential equation *y*' = (1 + *y*)/(1 – *y*) with any initial condition *y*(0) -:: 1. What happens here?