Hi,
I believe it is assessed under H3 Maths where the
integrating factor method is to be used to solve the question.
We rewrite the DE as
(dy/dx) - (cos x) y = (cos x) e^(sin x).
Integrating factor is e to the power of integral of -cos
x dx, leading to
e^(-sin x).
Multiplying both sides of the DE, we obtain
e^(-sin x) (dy/dx) - (cos x) e^(-sin x) y = cos x
=> d/dx [ y e^(-sin x) ] = cos x.
Integrating both sides wrt x, we obtain
y e^(-sin x) = integral of cos x dx
= sin x + c.
When x = 0 and y = 1, c = 1.
Now y e^(-sin x) = sin x + 1 is the particular solution,
from which we arrive at
y = (sin x + 1) e^(sin x).
Thanks and have a great reunion dinner without worrying
about this question :)
Cheers,
Wen Shih