Question

18. Applying charpit's methods q = 3p2 -​

Answer 1

Given :

q = 3p²

To find :

Solve using Charpit's method

Solution :

q = 3p²

f = 3p² - q

x, y, z are absent.

Therefore, $fx = fy = fz = 0$

By Charpit's Method,

        dp           =          dq           =            dz             =    dx   =     dy  

δf/δx + p.δf/δz   δf/δy + q.δf/δz   -p.δf/δp - q.δf/δq    -δf/δp    -δf/δq

   dp   =    dq     =     dz     = dx = dy

0 + p.0    0 + q.0    -6p² + q    -6p     1

dp = 0

Integrating, Taking p = a

q = 3a²

Substituting the values of p and q in dz = p.dx + q.dy

dz = adx + 3a²dy

After integration,

z = ax + 3a²y + b