The order and degree of the differential equation \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0\) are respectively

(a)

2, 3

(b)

3, 3

(c)

2, 6

(d)

2, 4

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 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)

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

The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

(a)

\(\frac { x }{ { e }^{ \lambda } } \)

(b)

\(\frac { { e }^{ \lambda} }{ x } \)

(c)

\({ \lambda e }^{ x }\)

(d)

e^x

The integrating factor of the differential equation \(\frac{d y}{d x}+P(x) y=Q(x)\) is x, then P(x)

(a)

x

(b)

\(\frac { { x }^{ 2 } }{ 2 } \)

(c)

\(\frac{1}{x}\)

(d)

\(\frac{1}{x^2}\)