(**) Consider the differential equation dy 5, dz with initial condition y(0) = 2. A. Use...

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(**) Consider the differential equation dy 5, dz with initial condition y(0) = 2. A. Use linear approximation (Euler's method) with two steps to estimate y when x = 1: y(1) (Be sure not to round your calculations at each step!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) B. What is the solution to this differential equation (with the given initial condition)? Hint: this is asking for a function that has a derivative of 52. What function do you have to start with to get that derivative? Try using your knowledge derivatives to guess the solution) C. What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = Note that in this example, the right hand side of the differential equation is a function of the independent variable instead of the dependent variabl Nonetheless you can apply Fuler's method. (**) Consider the differential equation dy 5, dz with initial condition y(0) = 2. A. Use linear approximation (Euler's method) with two steps to estimate y when x = 1: y(1) (Be sure not to round your calculations at each step!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) B. What is the solution to this differential equation (with the given initial condition)? Hint: this is asking for a function that has a derivative of 52. What function do you have to start with to get that derivative? Try using your knowledge derivatives to guess the solution) C. What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = Note that in this example, the right hand side of the differential equation is a function of the independent variable instead of the dependent variabl Nonetheless you can apply Fuler's method.