Question

x(y+4)+y' =0 y(0)=-5 ? separation of variable

Answer 1

We have:

`y' = -x(y + 4)`

`(y')/(y + 4) = -x`

`ln|y + 4| = -1/2x^2 + C`

`y + 4 = e^(-1/2x^2 + C)`

`y = e^(-1/2x^2 + C) - 4`

We now solve for `C`.

`-5 = e^(-1/2(0)^2 + C) - 4`

`-1 = e^C`

But no value of `C` satisfies so there must be a problem with the question.

Hopefully this helps!