# Trying to solve Navier equations with Maple

I've been trying for ages now to get this to work, it's a system of partial differential equations (Engineering, Plate theory)

$$pde1: = \frac{{{\partial ^2}}}{{\partial {x^2}}}u\left( {x,y} \right) + \frac{{1 - {\rm{\nu }}}}{2}\frac{{{\partial ^2}}}{{\partial {y^2}}}u\left( {x,y} \right) + \frac{{1 + {\rm{\nu }}}}{2}\frac{{{\partial ^2}}}{{\partial x\partial y}}v\left( {x,y} \right) = 0$$ $$pde2: = \frac{{{\partial ^2}}}{{\partial {y^2}}}v\left( {x,y} \right) + \frac{{1 - {\rm{\nu }}}}{2}\frac{{{\partial ^2}}}{{\partial {x^2}}}v\left( {x,y} \right) + \frac{{1 + {\rm{\nu }}}}{2}\frac{{{\partial ^2}}}{{\partial x\partial y}}u\left( {x,y} \right) = 0$$

Just solving the system works (not very useful though):

$$pdsolve\left( {\left\{ {pde1,pde2} \right\},\left\{ {u\left( {x,y} \right),v\left( {x,y} \right)} \right\}} \right)$$

However I with to supply some boundary conditions like clamping the plate at the left and top side:

$$bcs: = u\left( {0,y} \right) = 0,v\left( {x,0} \right) = 0$$

Then I want to solve it using:

$$pdsolve\left( {\left\{ {pde1,pde2,bcs} \right\},\left\{ {u\left( {x,y} \right),v\left( {x,y} \right)} \right\}} \right)$$

But Maple refuses to do it and displays:

Error, (in pdsolve/BC) not a differential equation with respect to {u(x, y), v(x, y)}

What am I doing wrong here? Thanks

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