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Mathematics 40 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

hey

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

THANK YOU SO MUCH!

OpenStudy (anonymous):

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

OpenStudy (anonymous):

i have the formula, its a bit long

OpenStudy (anonymous):

first we have to check that My = Nt ,

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

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