Using the Euler's Method discussed in the lecture: a) write a function called eulermethod that will...

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Using the Euler's Method discussed in the lecture: a) write a function called "eulermethod" that will (1) print out the corresponding y-value for a given x- value and (2) a plot of the original function y(x) for the following differential equation: [70] dy Vx +x'y° =1 dx %3D The function will receive: the initial conditions (i.e. xo and yo), the x-value and the step-size. Recall that the approximate solution for yn when x = Xn is given by the following equation, where h is the step-size and F(x,y) =y': Y, = Yn-1 + hF(xp-1»Yp-1) 'n-1: Start with the function definition shown below: function eulermethod (x0, y0, x, h) % COMMENT SECTION end Test your function by computing y(5), with y(0) = 0.5, and the step size is 0.001. %3D b) Now, modify the function that you created in part a) such that the function now will also plot the rate of change dyldx on the same graph, so that your graph should display both y(x) and dyldx for 0<x< 5. Include a legend in your graph. [30] Using the Euler's Method discussed in the lecture: a) write a function called "eulermethod" that will (1) print out the corresponding y-value for a given x- value and (2) a plot of the original function y(x) for the following differential equation: [70] dy Vx +x'y° =1 dx %3D The function will receive: the initial conditions (i.e. xo and yo), the x-value and the step-size. Recall that the approximate solution for yn when x = Xn is given by the following equation, where h is the step-size and F(x,y) =y': Y, = Yn-1 + hF(xp-1»Yp-1) 'n-1: Start with the function definition shown below: function eulermethod (x0, y0, x, h) % COMMENT SECTION end Test your function by computing y(5), with y(0) = 0.5, and the step size is 0.001. %3D b) Now, modify the function that you created in part a) such that the function now will also plot the rate of change dyldx on the same graph, so that your graph should display both y(x) and dyldx for 0<x< 5. Include a legend in your graph. [30]