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B.C's : ## \psi_{1} = \theta_{1} = 0 ## at both ## y=0## and ##y=1##. ##\nabla^2 = \partial^2/\partial x^2 + \partial^2/\partial y^2 ## Both ##\psi_{1} ## and ##\theta_{1}## are functions of x and y.

Yup. You may consider ## \psi ## inplace of ##\psi_1## and ## \theta ## in place of ##\theta_{1}##

HI HI! While trying to solve problem in Hydrodynamic stability I have got a system of Two Partial Diffential equations : Can anyone help me to solve this analytically? Is there any general method to solve system of PDEs?