solving the differential equation expressing y as x

Question

anonymous · Answer

f(x) has a x intercept at (2,0) and satisfies the differential equation
$$x^2e^y \frac{ dy }{dx } = 4$$
How am I suppose to solve the differential equation? Solve for the dy/dx and e^y on one side and then just find the antiderivative? I am tempted to just solve fro e^y but I think I can't for some reason.... please guide me :p

loser66 · Answer

not sure whether I can help or not, just try
separate the term
e^ydy = 4/x^2 dx
integral both sides

loser66 · Answer

so, $$e^y = \dfrac{-4}{x} +C$$
when x = 2, y =0 , replace to it to get C = 3
back to e^y = -4/x +3
ln both sides to get y = .....

anonymous · Answer

so... what happened exactly? when I tried to find the integral of a derivative such as dy/dx, it simply disappears?

loser66 · Answer

solving differential equation is to find out y which satisfies the problem. It's not the process to find out dy/dx

anonymous · Answer

Ah... Ok, but intergrating is the process of finding the antiderivative of an equation, so wouldn't dydx turn into y?

anonymous · Answer

Thanks... Anyhow I ahve at least understand what I am suppose to do now.