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 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 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

The degree of the differential equation \(\sqrt { 1+\left( \frac { { d }y }{ dx } \right) ^{ \frac { 1 }{ 3 } } } =\frac { { d }^{ 2 }y }{ dx^{ 2 } } \) is _____________

(a)

1

(b)

2

(c)

3

(d)

6

The degree of c =\(\frac { \left[ 1+\left( \frac { dy }{ dx } \right) ^{ 3 } \right] ^{ 2/3 } }{ \frac { d^{ 3 }y }{ dx^{ 3 } } } \) where c is a constant is _____________

(a)

1

(b)

3

(c)

-2

(d)

2

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 solution of xdx +ydy = 0 is

(a)

x²+y² = c

(b)

\(\frac{x}{y}\)= c

(c)

x²-y² = c

(d)

xy = c

The solution of \(\frac { dy }{ dx } \) = e^x-y is _____________

(a)

e^ye^x = c

(b)

y=log ce^x

(c)

y=log(e^x+c)

(d)

e^x+y = c

The solution of \(\frac { dp }{ dt } \) = ke^-t (k is a constant) is _____________

(a)

c-\(\frac { k }{ { e }^{ t } } \) = p

(b)

p = ke^t+c

(c)

t = log\(\left( \frac { c-p }{ k } \right) \)

(d)

t = log_c p

In (x²-y²)dy = 2xy dx, if we put y = vx, then the equation is transformed into _____________

(a)

\(\frac { 1+{ v }^{ 2 } }{ v+{ v }^{ 3 } } dv=\frac { dx }{ x } \)

(b)

\(\frac { 1{ -v }^{ 2 } }{ v(1+{ v }^{ 2 }) } dv=\frac { dx }{ x } \)

(c)

\(\frac { dv }{ { v }^{ 2 }-1 } =\frac { dx }{ x } \)

(d)

\(\frac { dv }{ 1+{ v }^{ 2 } } =\frac { dx }{ x } \)

The integrating factor of x\(\frac { dy }{ dx } \)-y = e^x is _____________

(a)

log x

(b)

e^-yx

(c)

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

(d)

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