Can anyone help me solve this diff eq? dy/dx = x(1+y) Thanks!?

Answer 1

dy/dx = x(1 + y)
Rearranging
dy/(1 + y) = xdx
Integrating botrh sides
ln(1 + y) = (x^2)/2 + c
(1 + y) = e^(x^2/2 + c) = e^(x^2/2)e^(c) = c*e^(x^2/2)
y = c*e^(x^2/2) - 1

Answer 2

∫ dy/(1 + y) = ∫ x dx
log (1 + y) = x²/2 + C

Answer 3

this can be done by separation of variables

dy/(y+1) = x dx
integraing we get

ln(y+1) = x^2/2 + c

or y + 1 = Ce^(x^2/2)
y = Ce^(x^2/2) - 1

Answer 4

it could be like this...
dy/dx=x+xy
dy/dx=1+y