# The Transformation of Partial Differential Equation

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Using the chain rule of partial differentiation, to show that the differential equation Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Au_xx + Bu_xy + Â Cu_yy + Du_x + Eu_y + Fu = G Â Â Â Â Â Â Â

Â Â transforms into the differential equation Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â A' u_,aa + B'u_bb + C'u_cc + Du_a + Eu_b + Fu = G Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â The complete problem is in the attached file.

Â© BrainMass Inc. brainmass.com December 24, 2021, 11:34 pm ad1c9bdddfhttps://brainmass.com/math/fourier-analysis/transformation-partial-differential-equation-581963

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The solution is in the attached file.

Â© BrainMass Inc. brainmass.com December 24, 2021, 11:34 pm ad1c9bdddf>https://brainmass.com/math/fourier-analysis/transformation-partial-differential-equation-581963