Solve the separable differential equation dy/dx=(x-10)e^(-y), given the initial conditions y(2)=ln(2), to find y(0)

Question

anonymous · Answer

wouldn't you jut use implicit differentiation and then substitute?

anonymous · Answer

ok
first you find a diff of y=ln(x), and replace in the equation, is most easy, sorry i dont have a good english

anonymous · Answer

$$dy = (x-10)dx*e^-(x)$$
$$e^y*dy = (x-10)dx$$

anonymous · Answer

then integrate both sides

anonymous · Answer

I'm not sure I understand. In my answer I used partial derivatives, but I'm not sure how I got the answer when I did it previously...

anonymous · Answer

fxx(x,y)=6x  and fyy(x,y)=2 and fxy(x,y)=-6, and I got D=6x(2)-(-6)^2=12x-36 which is the answer... but I don't know where I got 6x(2)-(-6)^2 from previously.

anonymous · Answer

^Sorry, the above post was meant for a different question.

anonymous · Answer

Frayar22, do you mean differentiate y=ln(x) ... y=1/x? I don't get it :(

anonymous · Answer

sorry , i have a mistake
sorry
forgive all i say

(sorry for my bad englsih)