The order and degree of the differential equation \(\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 } \) are respectively ______.

(a)

2 and 3

(b)

3 and 2

(c)

2 and 1

(d)

2 and 2

The integrating factor of the differential equation \(\frac{dx}{dy}+Px=Q\) is ______.

(a)

e^ഽPdx

(b)

^{\(\int P d x\)}

(c)

ഽPdy

(d)

e^ഽPdy

The complementary function of (D²+ 4)y = e^2x is ______.

(a)

(Ax +B)e^2x

(b)

(Ax +B)e^−2x

(c)

A cos 2x + B sin 2x

(d)

Ae^−2x+ Be^2x

The particular integral of the differential equation f(D)y = e^ax where f(D) = (D−a)² ______.

(a)

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

(b)

xe^ax

(c)

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

(d)

x²e^ax

The differential equation of all circles with centre at the origin is _____________

(a)

xdy +ydx = 0

(b)

xdy - ydx = 0

(c)

xdx + ydy = 0

(d)

xdx - ydy = 0

The differential equation obtained by eliminating a and b from y = a e^3x + b e^-3x is _____________

(a)

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

(b)

\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)-9y = 0

(c)

\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -9\frac { dy }{ dx } \)

(d)

\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)+9x = 0

The degree and order of \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -6\sqrt { \frac { dy }{ dx } } \)= 0 are _____________

(a)

2,1

(b)

1,2

(c)

2,2

(d)

1,1

The integrating factor of (1+x²)\(\frac { dy }{ dx } \)+xy = (1+x²)³ is _____________

(a)

\(\sqrt { 1+{ x }^{ 2 } } \)

(b)

log(1+x²)

(c)

e^tan-1x

(d)

log(tan^-1x)

The complementary function of the differential equations (D²-D)y = e^x is _____________

(a)

A+Be^x

(b)

(Ax+B)e^x

(c)

A+B^e-x

(d)

(A+Bx)e^-x

The P.I. of \(\frac { d^{ 2 }y }{ { dx }^{ 2 } } -6\frac { dy }{ dx } +9y\)=e^3x is ______

(a)

\(\frac { { e }^{ 3x } }{ 2! } \)

(b)

\(\frac { { x }^{ 2 }e^{ 3x } }{ 2! } \)

(c)

\(\frac { xe^{ 3x } }{ 2! } \)

(d)

9e^3x