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How to make decomposition of 2 fourth order differential equations on 4 equations of second order

$$C_1x''''+C_2x'''+C_3x''+C_4x'+C_5x-C_6y''-C_7y=0$$

$$D_1y''''+D_2y'''+D_3y''+D_4y'+D_5y-D_6x''-D_7x=0$$

Known constants $$C_i, D_i$$

Thank you in advance

2 Answers 2