abc.mw

> a1(x,y):=exp(x/2)*exp(y)/2;

a1(x, y) := 1/2*exp(1/2*x)*exp(y)

> b1(x,y):=0.7/(x*x*y*y+0.5);

b1(x, y) := .7/(x^2*y^2+.5)

> c1(x,y):=(4-exp(x)-exp(y/2))*2;

c1(x, y) := 8-2*exp(x)-2*exp(1/2*y)

> d1(x,y):=x*x+y;

d1(x, y) := x^2+y

> e1(x,y):=x*y*y;

e1(x, y) := x*y^2

> f1(x,y):=3*x+2*y;

f1(x, y) := 3*x+2*y

> u(x,y):=x*x*x+2*y*y*y+3*x*x*y+4*x*y*y+5*x*y+6*x+7*y+8;

u(x, y) := x^3+2*y^3+3*x^2*y+4*x*y^2+5*x*y+6*x+7*y+8

> ux(x,y):=diff(u(x,y),x);

ux(x, y) := 3*x^2+6*x*y+4*y^2+5*y+6

> uy(x,y):=diff(u(x,y),y);

uy(x, y) := 6*y^2+3*x^2+8*x*y+5*x+7

> uxy(x,y):=diff(ux(x,y),y);

uxy(x, y) := 6*x+8*y+5

> uxx(x,y):=diff(ux(x,y),x);

uxx(x, y) := 6*x+6*y

> uyy(x,y):=diff(uy(x,y),y);

uyy(x, y) := 12*y+8*x

> c(x,y):=a1(x,y)*uxx(x,y)+b1(x,y)*uxy(x,y)+c1(x,y)*uyy(x,y)+d1(x,y)*ux(x,y)+e1(x,y)*uy(x,y)+f1(x,y);

c(x, y) := 1/2*exp(1/2*x)*exp(y)*(6*x+6*y)+.7*(6*x+8*y+5)/(x^2*y^2+.5)+(8-2*exp(x)-2*exp(1/2*y))*(12*y+8*x)+(x^2+y)*(3*x^2+6*x*y+4*y^2+5*y+6)+x*y^2*(6*y^2+3*x^2+8*x*y+5*x+7)+3*x+2*y

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