The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\) ______.

(a)

1

(b)

2

(c)

3

(d)

4

The order and degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}-\sqrt{\left(\frac{d y}{d x}\right)}-4=0\) are respectively ______.

(a)

2 and 6

(b)

3 and 6

(c)

1 and 4

(d)

2 and 4

If y = cx + c− c³ then its differential equation is ______.

(a)

\(y=\frac { dy }{ dx } +\frac { dy }{ dx } -{ \left( \frac { dy }{ dx } \right) }^{ 3 }\)

(b)

\(y={ \left( \frac { dy }{ dx } \right) }^{ 3 }=x\frac { dy }{ dx } -\frac { dy }{ dx } \)

(c)

\(\frac { dy }{ dx } +y={ \left( \frac { dy }{ dx } \right) }^{ 3 }-x\frac { dy }{ dx } \)

(d)

\(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

The differential equation of y = mx + c is ______.(m and c are arbitrary constants) 

(a)

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

(b)

y = x \(\frac { dy }{ dx } \) + c

(c)

xdy + ydx = 0

(d)

ydx − xdy = 0

Solution of \(\frac { dy }{ dx } \) + Px = 0 ______.

(a)

x = ce^py

(b)

x = ce^−py

(c)

x = py + c

(d)

x = cy

The differential equation formed by eliminating A and B from y = e^−2x(A cos x + B sin x) is ______.

(a)

y₂ − 4y₁ + 5 = 0

(b)

y₂+ 4y – 5 = 0

(c)

y₂−4y₁−5= 0

(d)

y₂ + 4y₁ + 5 = 0

A homogeneous differential equation of the form \(\frac { dy }{ dx } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution, ______.

(a)

y = v x

(b)

v = y x

(c)

x = v y

(d)

x = v

The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) } \) is ______.

(a)

\(f\left( \frac { y }{ x } \right) =k.x\)

(b)

\(xf\left( \frac { y }{ x } \right) =k\)

(c)

\(f\left( \frac { y }{ x } \right) =ky\)

(d)

\(yf\left( \frac { y }{ x } \right) =k\)

The differential equation \(\left( \frac { dx }{ dy } \right) ^{ 2 }+5y^{ \frac { 1 }{ 3 } }\)= x is _____________

(a)

order 2 degree 

(b)

order 1 degree 2

(c)

order 1 degree 6

(d)

order 1 degree 3

The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is _____________ (k is negative).

(a)

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

(b)

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

(c)

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

(d)

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