Answer the following questions about this program: function problem4_12 t=0; 12 2 y= 1; 4 dt = 1e-4; s for i1:8e.3 t=t+dt; a=y; b = getb ( y, a, t, dt); k=1; while abs (b) le-4 10 c = getc (y, t , dt); y=y-b/c; b = ge tb (y,a,t,dt); k=k+1; if k20 12 13 15 16 17 18 19 end 20 break end end a1 Eunction b - getb (v, a, t, dt) b = y- a - dt*(y"2 + cos (y* t)); 22 23 24 25 function c=getc (y, t , dt) c = 1 -at* (2*y- t*sin (y* t)); (a) What differential equation is solved by this program? (b) What is the initial condition? (c) What does the variable a represent? (d) What does the variable b represent? (e) What does the variable c represent? (f) What numerical method is implemented by the for loop in lines 5-19? (g) What numerical method is implemented by the while loop in lines 10-18? (h) What is the purpose of the if block in lines 15-17? (i) What is the value of t at the end of the program? G) What type of continuation method is used? Answer the following questions about this program: function problem4_12 t=0; 12 2 y= 1; 4 dt = 1e-4; s for i1:8e.3 t=t+dt; a=y; b = getb ( y, a, t, dt); k=1; while abs (b) le-4 10 c = getc (y, t , dt); y=y-b/c; b = ge tb (y,a,t,dt); k=k+1; if k20 12 13 15 16 17 18 19 end 20 break end end a1 Eunction b - getb (v, a, t, dt) b = y- a - dt*(y"2 + cos (y* t)); 22 23 24 25 function c=getc (y, t , dt) c = 1 -at* (2*y- t*sin (y* t)); (a) What differential equation is solved by this program? (b) What is the initial condition? (c) What does the variable a represent? (d) What does the variable b represent? (e) What does the variable c represent? (f) What numerical method is implemented by the for loop in lines 5-19? (g) What numerical method is implemented by the while loop in lines 10-18? (h) What is the purpose of the if block in lines 15-17? (i) What is the value of t at the end of the program? G) What type of continuation method is used