U=e^(-x-3y)*sin(x+3y)
x+3y=t
u=e^(-t)*sin(t)=e^(-t)*(e^(it)-e^(-it))/2i=(e^(t*(i-1))-e^(t*(-i-1))/2i=
du/dt=((i-1)e^(t*(i-1))-(-i-1)*e^(t*(-i-1))/2i=
d^2u/dt^2=((i-1)^2e^(t*(i-1))-(-i-1)^2*e^(t*(-i-1))/2i=(-2i*e^(t*(i-1))-(2i)*e^(t*(-i-1))/2i=
(-e^(t*(i-1))-e^(t*(-i-1))=-2e^(-t)*cos(t)
du/dx=du/dt*dt/dx=du/dt*1
du^2/dx^2=du^y/dt^2*dt/dx=du^2/dt^2*1=-2e^(-t)*cos(t)
du/dy=du/dt*dt/dy=du/dt*3
du^2/dy^2=3*du^y/dt^2*dt/dy=du^2/dt^2*9=-2e^(-t)*cos(t)*9
du^2/dx^2+du^2/dy^2=-20e^(-t)*cos(t)=-20e^(-x-3y)*cos(x+3y)
равенство du^2/dx^2+du^2/dy^2=0 - не выполняется
2x^2y`=x^2+y^2
x=ro*cos(fi)
y=ro*sin(fi)
ro=корень(x^2+y^2)
fi=arctg(y/x)
dy/dx=dy/dro*dro/dx+dy/dfi*dfi/dx
=sin(fi)*1/(2*корень(x^2+y^2))-ro*cos(fi)*1/(1+(y/x)^2)*y/x^2=
=sin(fi)*1/(2*ro)-cos(fi)*1/(1+(tg)^2)*sin/(cos^2*ro)=
=1/ro*sin(fi)*(1/2-cos(fi))
2x^2y`=x^2+y^2 =>2*ro^2*cos^2(fi)*1/ro*sin(fi)*(1/2-cos(fi))=ro^2
2*ro^2*cos^2(fi)*1/ro*sin(fi)*(1/2-cos(fi))=ro^2
ro=cos^2(fi)*sin(fi)*(1-2cos(fi))
y=ro*sin(fi)=cos^2(fi)*sin^2(fi)*(1-2cos(fi))
x=ro*cos(fi)=cos^3(fi)*sin(fi)*(1-2cos(fi))