# Exercici 07.12

## apartat a)

kill(all)$

Eq1:3-y=y^x;

Eq1b:  3-y = y^0;    solve(Eq1b, y);

Eq1;        depends(y, x);

diff(Eq1, x);

expand(%);

Eq2: - Dy(x) = x*y^(x-1)* Dy(x)+y^x*log(y) ;

Eq2b:  -Dy(0) = 0*2^(0-1)*Dy(0) + 2^0*log(2);

solve(Eq2b, Dy(0));

m=m:-log(2);

x0=x0:0;        y0=y0:2;        
y-y0 = m*(x-x0);    y-y0 = (-1/m)*(x-x0);

## apartat b)

kill(all)$

Eq1:y=x - 2*log(y);

Eq1b:  1=x - 2*log(1);    solve(Eq1b, x);

Eq1;        depends(y, x);

diff(Eq1, x);

factor(%);

Eq2: Dy(x) = - (2*Dy(x) - y)/y ;

Eq2b:  Dy(0) = (1 - 2*Dy(0))/1 ;        solve(Eq2b, Dy(0));

m=m:1/3;

x0=x0:1;        y0=y0:1;        
y-y0 = m*(x-x0);    y-y0 = (-1/m)*(x-x0);