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

The differential equation satisfied by all the straight lines in xy plane is _____________

(a)

\(\frac { dy }{ dx } \)=a constant

(b)

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

(c)

y+ \(\frac { dy }{ dx } \) = 0

(d)

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

If y = k.e^λx then its differential equation where k is arbitrary constant is _____________

(a)

\(\frac { dy }{ dx } \)= λy

(b)

\(\frac { dy }{ dx } \)= ky

(c)

\(\frac { dy }{ dx } \)+ky = 0

(d)

\(\frac { dy }{ dx } \)= e^λx

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 differential equation formed by eliminating A and B from y = e^x (A cos x + B sin x) is _____________

(a)

y₂+y₁= 0

(b)

y₂-y₁ = 0

(c)

y₂-2y₁+2y = 0

(d)

y₂-2y₁-2y = 0