07sanjeewakaru

Well-known member
  • Feb 9, 2013
    5,520
    1,802
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    ලංකාවෙ අඩා...!
    Hello machnla,

    (∂f(x,y))/∂x=Axy+Bx^2........(1)
    (∂f(x,y))/∂y=Cy^2+Dxy^2.....(2)
    f(x,y) hoyanne kohomada?
    (∂f(x,y))/∂x=Axy+Bx^2;
    Meka Anukalanaya karanawa x wishayen....Partial defferentiate karaddi aneth variable eka ganan ganne ne wage...Aneth paththata y ganan nogena Anukalanaya karanawa.......

    f(x,y)=Ayx^2/2+Bx^3/3+f(y)

    Habai Abimatha niyathaya y matha rada pawathinawa...Eka niyathaknewei..Ei f(x,y),x,y wala function ekakne....(nikan function ekak anukalanaya karama dana niyathe variable eka matha rada pawathinne ne wage thama....)

    Dan meka y wishayen Patial differentiate karanawa.....Dan y witharai variable eka...

    (∂f(x,y))/∂y=Ax^2/2+f '(y)....(3)
    f(y) kiyanne y wala function ekakne..eka y walin awakalanaya karama...f '(y)..

    Dan meka (2) ta samana karanawa....
    Ax^2/2+f '(y)=Cy^2+Dxy^2
    f '(y)=Cy^2+Dxy^2-Ax^2/2
    Meka onama x,y walata true wenne....
    A=0,.....(4)
    D=0......(5)

    (f '(y) only depend on y not x)
    and....

    f '(y)=Cy^2...

    Dan meka normal differential equation ekak...Anukalaya karanta thiyenne...
    f(y)=Cy^3/3+k
    k..Abimatha niyathe....

    (3)n
    f(x,y)=Ayx^2/2+Bx^3/3+f(y)
    (4)n,
    A=0 ne..

    f(x,y)=Bx^3/3+Cy^3/3+k.....where k is a constant independent of x,y

    Oya mata therichcha hati....:):):):)
    Meka kohehari thibba ganakda..Neththan oya hithala damma ekakda....
    Kohomath hama A,B,C,D ekakatama f(x,y) hoyanta ba....:):):)
     
    Last edited:

    yaan

    Well-known member
  • Jun 13, 2007
    1,062
    240
    63
    Dehiwala
    (∂f(x,y))/∂x=Axy+Bx^2;
    Meka Anukalanaya karanawa x wishayen....Partial defferentiate karaddi aneth variable eka ganan ganne ne wage...Aneth paththata y ganan nogena Anukalanaya karanawa.......

    f(x,y)=Ayx^2/2+Bx^3/3+f(y)

    Habai Abimatha niyathaya y matha rada pawathinawa...Eka niyathaknewei..Ei f(x,y),x,y wala function ekakne....(nikan function ekak anukalanaya karama dana niyathe variable eka matha rada pawathinne ne wage thama....)

    Dan meka y wishayen Patial differentiate karanawa.....Dan y witharai variable eka...

    (∂f(x,y))/∂y=Ax^2/2+f '(y)....(3)
    f(y) kiyanne y wala function ekakne..eka y walin awakalanaya karama...f '(y)..

    Dan meka (2) ta samana karanawa....
    Ax^2/2+f '(y)=Cy^2+Dxy^2
    f '(y)=Cy^2+Dxy^2-Ax^2/2
    Meka onama x,y walata true wenne....
    A=0,.....(4)
    D=0......(5)

    (f '(y) only depend on y not x)
    and....

    f '(y)=Cy^2...

    Dan meka normal differential equation ekak...Anukalaya karanta thiyenne...
    f(y)=Cy^3/3+k
    k..Abimatha niyathe....

    (3)n
    f(x,y)=Ayx^2/2+Bx^3/3+f(y)
    (4)n,
    A=0 ne..

    f(x,y)=Bx^3/3+Cy^3/3+k.....where k is a constant independent of x,y

    Oya mata therichcha hati....:):):):)
    Meka kohehari thibba ganakda..Neththan oya hithala damma ekakda....
    Kohomath hama A,B,C,D ekakatama f(x,y) hoyanta ba....:):):)

    REP ++ :)
     

    supun44

    Active member
  • May 18, 2012
    267
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    28
    40
    Comoros
    ela ela macho thanks a lot
    avurudu ganakata kalin hadapuwa mathaka ne
    meka mokak hari pothaka ganak magenuth wena yaluwek ahuwe :)

    (∂f(x,y))/∂x=Axy+Bx^2;
    Meka Anukalanaya karanawa x wishayen....Partial defferentiate karaddi aneth variable eka ganan ganne ne wage...Aneth paththata y ganan nogena Anukalanaya karanawa.......

    f(x,y)=Ayx^2/2+Bx^3/3+f(y)

    Habai Abimatha niyathaya y matha rada pawathinawa...Eka niyathaknewei..Ei f(x,y),x,y wala function ekakne....(nikan function ekak anukalanaya karama dana niyathe variable eka matha rada pawathinne ne wage thama....)

    Dan meka y wishayen Patial differentiate karanawa.....Dan y witharai variable eka...

    (∂f(x,y))/∂y=Ax^2/2+f '(y)....(3)
    f(y) kiyanne y wala function ekakne..eka y walin awakalanaya karama...f '(y)..

    Dan meka (2) ta samana karanawa....
    Ax^2/2+f '(y)=Cy^2+Dxy^2
    f '(y)=Cy^2+Dxy^2-Ax^2/2
    Meka onama x,y walata true wenne....
    A=0,.....(4)
    D=0......(5)

    (f '(y) only depend on y not x)
    and....

    f '(y)=Cy^2...

    Dan meka normal differential equation ekak...Anukalaya karanta thiyenne...
    f(y)=Cy^3/3+k
    k..Abimatha niyathe....

    (3)n
    f(x,y)=Ayx^2/2+Bx^3/3+f(y)
    (4)n,
    A=0 ne..

    f(x,y)=Bx^3/3+Cy^3/3+k.....where k is a constant independent of x,y

    Oya mata therichcha hati....:):):):)
    Meka kohehari thibba ganakda..Neththan oya hithala damma ekakda....
    Kohomath hama A,B,C,D ekakatama f(x,y) hoyanta ba....:):):)