I need help with a differential equation (1+y^2)(e^(2x) dx - e^y dy)-(1+y)dy = 0

Question

anonymous · Answer

$$(1+y^2)(e ^{2x}dx - e^y dy) - (1 +y)dy=0$$

rational · Answer

that looks separable

janu16 · Answer

Are thete any answer choices?

anonymous · Answer

$$e ^{2x}dx - e^y dy = \frac{ dy + y dy }{ 1+y^2 }$$

anonymous · Answer

This is something new we are seeing in class and I'm unsure as to how I should approach it.

rational · Answer

collect terms attached to `dx` on one side
and terms attached to `dy` on other side

janu16 · Answer

Is that thr equation or answer choice?

anonymous · Answer

no answer choice

rational · Answer

get it into this form : 

(stuff) `dy` = (stuff) `dx`

anonymous · Answer

$$e ^{2x}dx = \frac{ dy+y dy }{ 1+y^2 }+ e^y dy$$

rational · Answer

all `dy` s must be on one side

rational · Answer

all `dx` must be on other side

anonymous · Answer

I have all dx on the left side and dy on the right side

rational · Answer

Ahh nice :) simply integrate now

rational · Answer

$$\int e ^{2x}dx = \int \frac{ (1+y) dy }{ 1+y^2 }+\int  e^y dy$$

anonymous · Answer

oo I see what you are doing.

anonymous · Answer

$$\frac{ 1 }{ 2 }e^{2x}=\tan^{-1}(y)+\frac{ 1 }{ 2 } \ln|1+y^2|+e^y $$

anonymous · Answer

@rational just a little question, is this all to it?meaning that this falls as a "separable category" where it ends as a general solution such as x(x) + y (y) = C?