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

(a)

2, 3

(b)

3, 3

(c)

2, 6

(d)

2, 4

The differential equation of the family of curves y = Ae^x + Be^−x, where A and B are arbitrary constants is

(a)

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

(b)

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

(c)

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

(d)

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

The solution of the differential equation \(2x\frac{dy}{dx}-y=3\) represents

(a)

straight lines

(b)

circles

(c)

parabola

(d)

ellipse

The degree of the differential equation \(y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....\) is

(a)

2

(b)

3

(c)

1

(d)

4

The solution of the differential equation \(\frac { dy }{ dx } +\frac { 1 }{ \sqrt { 1-{ x }^{ 2 } } } =0\) is

(a)

y + sin^-1 x = c

(b)

x + sin^-1 y = 0

(c)

y²+ 2 sin^-1 x = c

(d)

x²+ 2 sin^-1y= c

The number of arbitrary constants in the general solutions of order n and n +1 are respectively

(a)

n-1,n

(b)

n,n+1

(c)

n+1,n+2

(d)

n+1,n

The slope at any point of a curve y = f (x) is given by \(\frac{dy}{dx}=3x^2\) and it passes through (-1, 1). Then the equation of the curve is

(a)

y = x³ + 2

(b)

y = 3x² + 4

(c)

y = 3x⁴ + 4

(d)

y = 3x² + 5

The order and degree of the differential equation \({ \left[ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +\left( \frac { dy }{ dx } \right) \right] }^{ \frac { 1 }{ 2 } }=\frac { { d }^{ 3 }y }{ { dx }^{ 3 } } \) are __________

(a)

1, 2

(b)

2, 1

(c)

3, 2

(d)

2, 3

The solution of sec²x tan y dx + sec²y tan x dy = 0 is _________

(a)

tan x+tan y = c

(b)

sec x + sec y = c

(c)

tan x tan y = c

(d)

sec x- sec y = c

The transformation y = vx reduces \(\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x } \) __________ 

(a)

\(\frac { 3av }{ 4v+1 } =\frac { dx }{ x } \)

(b)

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

(c)

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

(d)

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