Differetialgleichung§für§u=EModul λ Derivative[1, 1][u][x, y]==EModul (1 + Inv0 + Inv0 (λ^2)) (Inv0 Derivative[0, 2][u][x, y]+(1 + Inv0) Derivative[2, 0][u][x, y])

Differetialgleichung§für§v=EModul λ Derivative[1, 1][v][x, y]==EModul (Inv0 + (1 + Inv0) (λ^2)) ((1 + Inv0) Derivative[0, 2][v][x, y]+Inv0 Derivative[2, 0][v][x, y])

Lösung$u$C = DSolve[
            Differetialgleichung§für§u, 
            u[x, y], {x, y}][[1, 1, 2]] // FullSimplify

Lösung$v$C = DSolve[
            Differetialgleichung§für§v, 
            v[x, y], {x, y}][[1, 1, 2]] // FullSimplify