Differential equation:

1. given y'=y+x; y(0)=1.

(a) using picard's method, give the first five terms of the iterative solution starting with latex: y_0\left(x\right)=1 y 0 ( x ) = 1 .

(b) using picard's method, give the first five terms of the iterative solution starting with latex: y_0\left(x\right)=x y 0 ( x ) = x .

(c) based on your answers, do different initial guess functions lead to different outcomes?

(d) solve the equation exactly and use power series expansion to compare it with the iterative solutions in (a) and (b).

for the points! : )

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)

the 3rd on is correct

step-by-step explanation:

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d