Solve partial differential equation $F = zp(x+y)+q^2-pq-z^2=0$

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Solve partial differential equation $$F = zp(x+y)+q^2-pq-z^2=0, p = fracpartial zpartial x, q = fracpartial zpartial y$$




My attempt:



Charpit's equations gives:



$$fracdx-z(x+y) = fracdyp-2q = fracdpp^2(x+y)-pz-q = fracdqzp-q(p-2q) = fracdz(p-2q)q-pz(x+y) $$



Taking $dx, dy, dz$ terms, i got $$dz=pdx+qdy$$



How to proceed further?




pde




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    Solve partial differential equation $$F = zp(x+y)+q^2-pq-z^2=0, p = fracpartial zpartial x, q = fracpartial zpartial y$$




    My attempt:



    Charpit's equations gives:



    $$fracdx-z(x+y) = fracdyp-2q = fracdpp^2(x+y)-pz-q = fracdqzp-q(p-2q) = fracdz(p-2q)q-pz(x+y) $$



    Taking $dx, dy, dz$ terms, i got $$dz=pdx+qdy$$



    How to proceed further?




    pde




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite












      Solve partial differential equation $$F = zp(x+y)+q^2-pq-z^2=0, p = fracpartial zpartial x, q = fracpartial zpartial y$$




      My attempt:



      Charpit's equations gives:



      $$fracdx-z(x+y) = fracdyp-2q = fracdpp^2(x+y)-pz-q = fracdqzp-q(p-2q) = fracdz(p-2q)q-pz(x+y) $$



      Taking $dx, dy, dz$ terms, i got $$dz=pdx+qdy$$



      How to proceed further?




      pde




      share|cite|improve this question














      Solve partial differential equation $$F = zp(x+y)+q^2-pq-z^2=0, p = fracpartial zpartial x, q = fracpartial zpartial y$$




      My attempt:



      Charpit's equations gives:



      $$fracdx-z(x+y) = fracdyp-2q = fracdpp^2(x+y)-pz-q = fracdqzp-q(p-2q) = fracdz(p-2q)q-pz(x+y) $$



      Taking $dx, dy, dz$ terms, i got $$dz=pdx+qdy$$



      How to proceed further?





      pde





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited 6 hours ago









      Davide Morgante

      1,566118




      1,566118









      asked 7 hours ago









      Magneto

      703111




      703111

























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