Question

15) if p+ sinq=0 then complete integral be​

Answer 1

Given ,

$p + \sin(q) = 0$

to find,

The complete integral

solution :

let ,

$f(p,q) = p + \sin(q) = 0$.(1)

$f(p,q) \: does \: not \: contain \: xyz \: then \: put \\ p = a \: or \: q = a$

putting q = a in equation 1 we get,

p + sin(a) = 0

p = - sin(a)

=> dz = pdx + qdy

integrating both the side

=> ∫dz = ∫pdx + ∫qdy

=> z = ∫-sin(a) dx + ∫a dy

=> z = - x sin(a) + ya

Therefore ,

The complete integral is z = - x sin(a) + ya

Answer 2

Given ,

$p + \sin(q) = 0$

to find,

The complete integral

solution :

let ,

$f(p,q) = p + \sin(q) = 0 \: ...........(1)$

$f(p \: q) \: does \: not \: contain \: xyz \: then \: put\\ p = a \: or \: q = a$

putting q = a in equation 1 we get,

$p + \sin(a) = 0$

$p = - \sin(a)$

$dz = pdx + qdy$

integrating both the side

$∫dz = ∫pdx + ∫qdy$

$z = ∫-sin(a) dx + ∫a dy$

$z = - x sin(a) + ya$

Therefore ,

The complete integral is z = - x sin(a) + ya