Question

solve by charpits method; q=px+p2​

Answer 1

Step-by-step explanation:

q=px+p2 slove by charpits method

Answer 2

Answer:

q+xp-p^2=0

∂f/∂p=(x-2p),

∂f/∂q=1,

∂f/∂x=p,

∂f/∂y=0,

∂f/∂z=0

dx/(-∂f/∂p)=dy/(-∂f/∂q)=dz/(-p ∂f/∂p-q ∂f/∂q)=dp/(∂f/∂x+p ∂f/∂z)+dq/(∂f/∂y+q ∂f/∂z)=(∂∅)/0

dx/(-(x-2p) )=dy/(-1)=dz/(-p(x-2p)-q)=dp/p=dq/0=(∂∅)/0 dy/(-1)=dp/p

log⁡p=-y+log⁡a

p=ae^(-y)

q+xae^(-y)=(ae^(-y) )^2

q=a^2 e^(-2y)-xae^(-y)

dz=pdx+qdy

dz=ae^(-y) dx+a^2 e^(-2y)-xae^(-y) dy

dz=a(e^(-y) dx-xe^(-y) dy)+a^2 e^(-2y) dy

z=axe^(-y)-1/2 a^2 e^(-2y)+b

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