(∂f(x,y))/∂x=Axy+Bx^2;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
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 '....(3)
fkiyanne y wala function ekakne..eka y walin awakalanaya karama...f '
..
Dan meka (2) ta samana karanawa....
Ax^2/2+f '=Cy^2+Dxy^2
f '=Cy^2+Dxy^2-Ax^2/2
Meka onama x,y walata true wenne....
A=0,.....(4)
D=0......(5)
(f 'only depend on y not x)
and....
f '=Cy^2...
Dan meka normal differential equation ekak...Anukalaya karanta thiyenne...
f=Cy^3/3+k
k..Abimatha niyathe....
(3)n
f(x,y)=Ayx^2/2+Bx^3/3+f
(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....![]()


(∂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
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 '....(3)
fkiyanne y wala function ekakne..eka y walin awakalanaya karama...f '
..
Dan meka (2) ta samana karanawa....
Ax^2/2+f '=Cy^2+Dxy^2
f '=Cy^2+Dxy^2-Ax^2/2
Meka onama x,y walata true wenne....
A=0,.....(4)
D=0......(5)
(f 'only depend on y not x)
and....
f '=Cy^2...
Dan meka normal differential equation ekak...Anukalaya karanta thiyenne...
f=Cy^3/3+k
k..Abimatha niyathe....
(3)n
f(x,y)=Ayx^2/2+Bx^3/3+f
(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....![]()
ela ela macho thanks a lot
avurudu ganakata kalin hadapuwa mathaka ne
meka mokak hari pothaka ganak magenuth wena yaluwek ahuwe![]()

