First-Order Linear PDE

Hello!

I've got the following problem:

Find the solution to the following IVP:

$v_y(x,y)+cv_x(x,y)=u(x,y)$ satisfying $v(x,0)=v_0(x)$

where $v_0\in C^1(\mathbb{R})$, $u\in C^1(\mathbb{R}^2)$ and the constant $c\in \mathbb{R}$.
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I tried to diff. once in $x$ and once in $y$ but couldn't see how that would help.