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2) $xu_x+u_y+uy=0,\,x\in\mathbb R,\,y>0$ and $u(x,0)=F(x),\,x\in\mathbb R.$

3) Solve the following equation $2xu_y-u_x=4xy,$ where the initial curve is given by $x=0,\,y=s,\,z=s.$

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1) Laplace transform or Fourier transform? Can I try separation of variables?

2) Same as 1).

3) I don't get the part of the initial curve, what does it mean?