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 differential equation formed by eliminating a and b from \(y=a e^{x}+b e^{-x}\) is ______.

(a)

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

(b)

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

(c)

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

(d)

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

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 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

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

y = mx

(1)

\(e^{ \int { pdy } }\)

Degree of linear differential equation

(2)

Family of lines

General form of linear equation

(3)

\(\frac { dy }{ dx } \)+Py = Q

I.F. of \(\frac { dy }{ dx } \)+Px = Q

(4)

\(e^{ \int { pdx } }\)

I.F. of \(\frac { dy }{ dx } \)+Py = Q

(5)

1