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The graph of the function $y=f(x)$ passing through the point $(0,1)$ and satisfy the differential equation $\large\frac{dy}{dx}$$+y \cos x =\cos x $ is such that

(a) It is even function

(b) It is odd function

(c) It is periodic

(d) It is not a cubic equation in d

Can you answer this question?

1 Answer

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$\large\frac{dy}{dx}$$+y \cos x =\cos x$
$I.F= e^{\int cos x dx} =e^{t \sin x}$
$y e^{t \sin x}=\int \cos x e^{t \sin x}dx$
$+\sin x =t$
$+ \cos x dx=dt$
$y e^{+\sin x}=+\int e^t dt+c$
$ye^{+ \sin x } =+e^t dt+c$
Passing through (0,1)
$1 e^{0}=+ e^{0}+c$
$y e^{\sin x} =e^{\sin x}+ 0$
$y=1$ constant function
Neither even nor odd
not periodic
Hence d is the correct answer.
answered Feb 5, 2014 by meena.p

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