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