Consider the differential equation B y 1 Be sure not to round your calculations at each step Now use four steps with initial

Question

Consider the differential equation B y 1 Be sure not to round your calculations at each step Now use four steps with initial condition y 0 2 A Use linear approximation Euler s method with two steps to estimate y when x 1 dy da B Magnitude of error in Euler with 2 steps 52 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 5x 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 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 Euler s method

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