z^2=pqxy solve by using charpits method?
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Let the given equation be f(z,p,q)=0 i.e, z^2-pqxy=0 perform derivation w.r.t p,q,x,y,z
then write charpits relation dx/-fp =dy/-fq =dz/(-p*fp-q*fq) =dp/(fx+x*fz) =dq/(fy+y*fz)
where fp,fq,fx,fy,fz are derivatives of z^2-pqxyAfter substitutions equate 1 and three equations i.e dx/(qxy)=dz/(2pqxy) Now u can find the value of p=(z+c)/(2*x) put p in z^2-pqxy=0You can find q=2*z^2/((z+c)*y) put the p,q in dz=pdx+qdy and integrate u can get the solution.
then write charpits relation dx/-fp =dy/-fq =dz/(-p*fp-q*fq) =dp/(fx+x*fz) =dq/(fy+y*fz)
where fp,fq,fx,fy,fz are derivatives of z^2-pqxyAfter substitutions equate 1 and three equations i.e dx/(qxy)=dz/(2pqxy) Now u can find the value of p=(z+c)/(2*x) put p in z^2-pqxy=0You can find q=2*z^2/((z+c)*y) put the p,q in dz=pdx+qdy and integrate u can get the solution.
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