Question

What happens after this..?

use separation of variables to solve the initial value problem

Answer 1

Forgot the parenthesis: e^( (x^2/2) + 2x + c)

Answer 2

sub youe initial values and solve for C
y= C(e^( .5x^2 + 2x ))- 5
for x = 0, y = 1
1 = C - 5
C = 6
so
y= 6e^( .5x^2 + 2x )- 5

Answer 3

ln(6)=c

Answer 4

How did you bring C out?

Answer 5

e^C = C
its math magic

Answer 6

? Huh?
But for example, e^(2) does not equal to 2...