Determine the solution of y′=−yy' = -yy′=−y with y(0)=10y(0) = 10y(0)=10.
y=10ety = 10e^ty=10et
y=10e−ty = 10e^{-t}y=10e−t
y=e−t+9y = e^{-t} + 9y=e−t+9
y=10−ty = 10 - ty=10−t