Question

How would I use an exact differential equation to solve dy/dt=((-e)^y)/(t(e^y)+2y)?

Answer 1

hey

Answer 2

get it into M(x,y)dx + N(x,y)dy = 0

Answer 3

How? I've only ever seen this type of equation as a very simple example already in the form M(x,y)dx + N(x,y)dy = 0. How would I separate this one?

Answer 4

or M(t,y) dt + N(t,y)dy = 0

Answer 5

i have dy(t e^y + 2y ) = (-e^y dt

Answer 6

so you start it like the solution to a separable function?

Answer 7

so e^y dt + (te^y + 2y ) dy = 0

Answer 8

THANK YOU SO MUCH!

Answer 9

I don't know why I couldn't separate that on my own.

Answer 10

i have the formula, its a bit long

Answer 11

first we have to check that My = Nt ,

Answer 12

the partial of M(t,y) with respect to y

Answer 13

deriv wrt to y M(t,y) = e^y
and deriv wrt to y N(t,y) = e^y , so its an exact equation

Answer 14

here http://www.twiddla.com/493184