Hi guys! I have to solve this equation. Actually the professor needs us to find the $\Lambda$ and I don't know if my steps are right. Can someone help me please? I'm not a physics student, I'm a mathematician, so this kind of staff is too high level for me.

$A(x,y) = \nabla \Lambda(x,y)=\Lambda x + \Lambda y$

If $n=x-y, z=y$

$\lambda (z,n) = \Lambda (x,y)$

$\Lambda y = \lambda z - \lambda n, \Lambda x = \lambda n$

$\Rightarrow \lambda z(z,n) = \Lambda (n+z, z)$

$\Rightarrow \int^z_{z_0} \lambda z(\delta , n) d\sigma = \int^z_{z_0} f (n+\sigma,\sigma)\;d\sigma$

$\lambda (z,n)-\lambda (z_0,n)=\int^z_{z_0} f(n+\sigma ,\sigma ) \; d\sigma$

$\Rightarrow \Lambda (x,y) - \Lambda(x-y, y_0) = \int^y_{y_0} f(x-y+\sigma,\sigma)\; ds$

$\Rightarrow \Lambda(x,y) = \Lambda(x-y,y_0)+\int^y_{y_0} f(x-y+\sigma,\sigma)\;ds$

Thanks :)