a) Formulate the differential equation being solved. b) What is the initial condition? c) What is...

 

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a) Formulate the differential equation being solved. b) What is the initial condition? c) What is the stepsize? d) What numerical methods are implemented in the for-loop (Lines 6-21)? e) What numerical methods are implemented in the while-loop (Lines 11-19)? f) What is the time horizon over which the differential equation is being integrated? function HW5.P1 1 2 y = 2; 3 t = 0; 4 dt = le-2; 5 n = 1e3; 6 ysol = zeros(n,1); 7 for i=1:n 8 9 10 11 12 13 14 15 16 17 t = t + dt; yt = y; z=getz (y,yt,y,dt); k = 1; while abs(z)>le-8 xgetx (y,t, dt); y=y-2/x; z=getz (y, yt,t,dt); k = k + 1; if k>30 18 19 20 21. break end end ysol (i) = y; 22 end 23 plot (linspace (0, dt n,n),ysol) 24 end 25 function r getz (y,yt,t,dt) 26 ryytdt log ((y 3-2+y^2+3+y)) *exp(-1); 27 end 28 function dr getx (y,t,dt) 29 dr 1-dt (3*y 2-4 y+3)/(y 3-2+y^2+3+y) *exp(-t); 30 end a) Formulate the differential equation being solved. b) What is the initial condition? c) What is the stepsize? d) What numerical methods are implemented in the for-loop (Lines 6-21)? e) What numerical methods are implemented in the while-loop (Lines 11-19)? f) What is the time horizon over which the differential equation is being integrated? function HW5.P1 1 2 y = 2; 3 t = 0; 4 dt = le-2; 5 n = 1e3; 6 ysol = zeros(n,1); 7 for i=1:n 8 9 10 11 12 13 14 15 16 17 t = t + dt; yt = y; z=getz (y,yt,y,dt); k = 1; while abs(z)>le-8 xgetx (y,t, dt); y=y-2/x; z=getz (y, yt,t,dt); k = k + 1; if k>30 18 19 20 21. break end end ysol (i) = y; 22 end 23 plot (linspace (0, dt n,n),ysol) 24 end 25 function r getz (y,yt,t,dt) 26 ryytdt log ((y 3-2+y^2+3+y)) *exp(-1); 27 end 28 function dr getx (y,t,dt) 29 dr 1-dt (3*y 2-4 y+3)/(y 3-2+y^2+3+y) *exp(-t); 30 end