The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters,is

(a)

\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0\)

(b)

\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }+y=0\)

(c)

\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }=0\)

(d)

\(\frac { { d }^{ 2 }x }{ { dy }^{ 2 } }=0\)

The general solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } \) is

(a)

xy = k

(b)

y = k log x

(c)

y = kx

(d)

log y = kx

The solution of \(\frac{d y}{d x}+p(x) y=0\) is

(a)

\(y={ ce }^{ \int { pdx } }\)

(b)

\(y={ ce }^{ -\int { pdx } }\)

(c)

\(x={ ce }^{ -\int { pdy } }\)

(d)

\(x={ce }^{ \int { pdy } }\)

If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\) When

(a)

p < q

(b)

p = q

(c)

p > q

(d)

p exists and q does not exist

If sin x is the integrating factor of the linear differential equation \(\frac { dy }{ dx } +Py=Q,\) then P is

(a)

log sin x

(b)

cos x

(c)

tan x

(d)

cot x

The solution of (x² - ay)dx = (ax - y²)dy is ___________

(a)

y = x²+y²-a(x+y)

(b)

y = x²+y²-a(x+y)

(c)

x³+y² = 3ayx+c

(d)

(x²-ay)(ax-y²) = 0

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 population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

(a)

\(\frac{dp}{dt}=\frac{k}{p}\)

(b)

\(\frac{dp}{dt}=kt\)

(c)

\(\frac{dp}{dt}=kp\)

(d)

\(\frac{dp}{dt}=-kp\)

Using y = vx, the differential equation \(\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } } \) is reduced to ________.

(a)

x(1+\(\sqrt{v}\))dv = v\(\sqrt{v}\)dx

(b)

x(1-\(\sqrt{v}\))dv = v\(\sqrt{v}\)dx

(c)

x(1+\(\sqrt{v}\))dv = -v\(\sqrt{v}\)dx

(d)

v(1+\(\sqrt{v}\))dx - v\(\sqrt{v}\)dv = 0

The differential equation associated with the family of concentric circles having their centres at the origin is _________.

(a)

\(\frac { dy }{ dx } =\frac { -x }{ y } \)

(b)

\(\frac { dy }{ dx } =\frac { -y }{ x } \)

(c)

\(\frac { dy }{ dx } =\frac { x }{ y } \)

(d)

\(\frac { dy }{ dx } =\frac { y }{ x } \)