Hi!

I'm stuck with a problem, it says:

Determine (if possible) a first order lineal partial differential equation that has as solutions

u_{1}(x,y)=x^2+y+sin(x+2y)

u_{2}(x,y)=x^2+y+cosh(\sqrt[5]{(x+2y)})

u_{3}(x,y)=-(x+2y)^4+(x^2+y)

I suppose that I am given the variable change \xi(x,y) = x+2y so the pde should look like

-2u_{x}(x,y) + u_{y}(x,y)+cu(x,y)=F(x,y)

where c \in \mathbb{R}

Now, should I check the conditions \{u_{i} \} impose on the pde and solve for c and F(x,y) ?

Thanks in advice