) 1. Consider the following initial value problem. Perform each of the following

Question

) 1. Consider the following initial value problem. Perform each of the following tasks (a) Without solving the problem, determine the interval of existence. Draw a number line, place any discontinuities on the number line, then place the independent value of the initial condition on the number line. Use the proper interval notation to state the interval of existence based on your number line. (b) Solve the initial value problem by hand, without the use of software of any kind. Make sure your answer is an explicit solution, not an implicit solution. (c) Use Matlab's plot command (not fplot) to draw your hand-calculated solution over the interval of existence (Caution: Make sure you use element-wise operators such as .*, -/, and., where needed). Hint: If the interval of eristence is something like (5, oo) (which it isn't for this problem), we should try something like plotting over the interval (5, 15), and if we want to see more, maybe (5,25). Keep playing with the interval until you get a picture that shous the eventual behavior of the answer. Use grid on, xlabel, ylabel, and title to decorate your image. Use the axis([xmin,xmax,ymin,ymax command to set the axes. Submit a printout of the resulting graph as well as a printout of your code with your quiz. (d) Use Matlab's fplot command (not plot) to draw the solution provided by the dsolve command over the interval of existence. Hint: If the interval of eristence is something like (5, oo) (uwhich it isn't for this problem), we should try something like plotting over the interval (5, 15), and if we want to see more, maybe (5, 25). Keep playing with the interval until you get a picture that shous the eventual behavior of the answer. Use grid on, xlabel, ylabel, and title to decorate your image. Use the axis([xmin,xmax,ymin,ymax]) command to set the axes. Make sure you use the same axis settings as you used in your plot command in part (c). Submit a printout of the resulting graph as well as a printout of your code with your quiz.

Explanation / Answer

first specify the interval over which the function exists by puttin within [] start and end of interval then solve the differential equation by using dsolve plot the curve using plot syms x(t) ode = diff(x,t) == (sin(2t)-x)/(t-2) xSol(t) = dsolve(ode) t = [0:0.1:2*pi] a = sin(t); plot(t,a)

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