I found the integrating factor μ= e^-[ln(x-ysiny)]= 1/(x-ysiny) but after that,
δM/δy is still not equal to δN/δx when I multiplied with μ...
1dx + (x/y-siny)dy = 0 ---> not exact
M(x,y) = 1 and N(x,y) = (x/y - siny)
δM/δy = 0 and δN/δx = (1/y)
To find the integrating factor;
g(x) = (1/N)*(δM/δy - δN/δx) and μ = exp[∫g(x)dx]
g(x) = 1/(x/y-siny)*(0-(1/y)
= 1/(x/y-siny)*(-1/y)
∫g(x)dx = ∫[-1/y / (x/y - siny)]dx = -ln(x-ysiny)
μ= e^-[ln(x-ysiny)]= 1/(x-ysiny)
but I couldn't figure out the rest of the question... Is there an error or someting? I'm not sure...Can anyone help me to solve this question?