### Mathematics - Differential Equations

#### Question - 1

The order and degree of the differential equation, ${ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 2 }+\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } }$= 4, are respectively

• A 2, 3
• B 3, 2
• C 3, 1
• D NONE OF THESE

#### Question - 2

The order and degree of the differential equation $\frac { { d }^{ 2 }s }{ d{ r }^{ 2 } } +3{ \left( \frac { ds }{ dt } \right) }^{ 2 }$ = t $\log { \left( \frac { { d }^{ 2 }s }{ d{ r }^{ 2 } } \right) }$, respectively are

• A 2, 2
• B 2, 1
• C 2, 3
• D NONE OF THESE

#### Question - 3

The degree of the differential equation ${ \left( \frac { { d }^{ 3 }y }{ { dx }^{ 3 } } \right) }^{ 4/3 }+3\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +\frac { dy }{ dx }$ + 1 = 0, is

• A 3
• B 4
• C 2
• D NOT DEFINED

#### Question - 4

The degree and the order of the differential equation $\frac { { d }^{ 2 }y }{ x{ d }^{ 2 } } +\frac { 2 }{ \left( \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right) }$+ 4y = 0 are

• A 2, 2
• B 4, 2
• C 2, 4
• D 2, 1

#### Question - 5

The differential equation representing the family of curves y2 = 2c(x + $\sqrt { c }$), where c is a positive parameter, is of order

• A 1
• B 2
• C 3
• D 4

#### Question - 6

A solution of the differential equation ${ \left( \frac { dy }{ dx } \right) }^{ 2 }-x\frac { dy }{ dx }$+ y = 0, is

• A y = 2
• B y = 2x
• C y = 2x - 4
• D y = 2x2 - 4

#### Question - 7

The order of the differential equation whose general solution is given by y = (c1 + c2) sine (x + c3) - c1ex + c5, is

• A 5
• B 4
• C 2
• D 3

#### Question - 8

If y1 and y2 are solutions of a differential equation then which of the following is also the solution of the differential equation

• A c1y1 + c2y2
• B $\frac { { y }_{ 1 } }{ { y }_{ 2 } }$
• C y1y2
• D ${ y }_{ 1 }^{ 2 }+{ y }_{ 2 }^{ 2 }$

#### Question - 9

The differential equation representing the family of curves given by the equation y = Aex + Be-x + C, is

• A $\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =y$
• B $\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =\frac { dy }{ dx }$
• C $\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } }$
• D ${ \left( \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right) }^{ 2 }+y=0$

#### Question - 10

The displacement x of a particle moving in a straight line at time t is given by the relation $x=A\sin { \left( \mu t+k \right) }$ The differential equation representing this phenomenon is

• A $\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } =-kx$
• B $\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } =kx$
• C $\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } ={ u }^{ 2 }x$
• D $\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } -{ u }^{ 2 }x$