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)

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

The solution of \(\frac{dy}{dx}+y\) cot x = sin 2x is ___________

(a)

y sin x = \(\frac{2}{3}\)sin³x+c

(b)

y sec x = \(\frac{x^2}{2}+c\)

(c)

y sin x = c+x

(d)

2y sin x = sin x - \(\frac{sin\ 3x}{3}+c\)

The I.F of y log y \(\frac{dx}{dy}+x-log\ y=0\) is __________

(a)

log(log y)

(b)

log y

(c)

\(\frac{1}{log\ y}\)

(d)

\(\frac{1}{log(log\ y)}\)

The order and degree of y'+(y")² = (x + t")² are _________.

(a)

1, 1

(b)

1, 2

(c)

2, 1

(d)

2, 2