Question

Using separation of variables technique, solve the following differential equation with initial condition y’ = e^y sinx and y(-pi) = 0.

The solution is: (see attachment)

Answer 1

ok so we got y' = e^y(sinx) --> dy/dx=e^y(sinx) --> (1/e^y)dy=sinxdx --> (e^-y)dy=sinxdx

so now we integrate both sides which is -(e^-y) = -cosx + c and now using y(-pi) = 0 says x=-pi, y=0 sub it in to find 0. so therefore -1=1 + c so c =-2 and -(e^-y) = -cosx - 2 = e^-y = cosx + 2 answer is C

Answer 2

did anybody tell you that you are a genius? :)

Answer 3

lol thanks

Answer 4

@Aka_966