Question

Please help me!

If y'= x(1 + y) and y > -1 , then y =

Please see the attachment (Thank You)

Answer 1

Seperate the variables, so everything with y and y' on one side, x on the other.

Answer 2

Not sure what you mean.

you start with y'= x(1 + y), then you divide or multiply both sides by the same things until you've separated the variables. I'd divide both sides by 1+y

Answer 3

This is just the first step, so now we have:
\[\frac{y'}{1+y}=x\]

Answer 4

The variables are now seperated. Now the following holds:
\[\int\frac{1}{1+y}dy=\int x dx\]

Answer 5

Can you compute both sides?

Answer 6

1/2 x^2 + C

Answer 7

Do you agree with that? What's the left side?