If cosx is an integrating factor of the differential equation \(\frac{dy}{dx}+Py= Q\), then P = ___________

(a)

-cot x

(b)

cot x

(c)

tan x

(d)

-tan x

The I.F. of cosec x \(\frac{dy}{dx}+y\) sec² x = 0 is ___________

(a)

e^{sec x}

(b)

e^tan x

(c)

e^{sec x tan x}

(d)

e^{sec2 x}

The general solution of \(4\frac{d^2 y}{dx^2}\) + y = 0 is _________

(a)

\(y={ e }^{ \frac { x }{ 2 } }\left[ A\ cos\frac { x }{ 2 } +B\ sin\frac { x }{ 2 } \right] \)

(b)

\(y={ e }^{ \frac { x }{ 2 } }\left[ A\ cos\frac { x }{ 2 } -B\ sin\frac { x }{ 2 } \right] \)

(c)

\(y=Acos\frac { x }{ 2 } +Bsin\frac { x }{ 2 } \)

(d)

\(y={ Ae }^{ \frac { x }{ 2 } }+B{ e }^{ \frac { -x }{ 2 } }\)

The I.F of \(\frac{dy}{dx}-y\) tan x = cos x is _________

(a)

sec x

(b)

cos x

(c)

e^{tan x}

(d)

cot x

The solution of log \(\left( \frac { dy }{ dx } \right) \) = ax + by is______.

(a)

\(\frac { { e }^{ ax } }{ a } +\frac { { e }^{ -by } }{ b } +c=0\)

(b)

ae^ax- be^-by + c = 0

(c)

ae^x + be^y = k

(d)

be^ax + ae^-by = k