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1 o . A nonhomogeneous linear equation of the fourth order has the form 1 f 4 y x x x x ′ ′ ′ ′ + f 3 y x x x ′ ′ ′ + f 2 y x x ′ ′ + f 1 y x ′ + f 0 y = g ( x ) , f k = f k ( x ) $$ f_{4} y_{xxxx}^{''''} + f_{3} y_{xxx}^{'''} + f_{2} y_{xx}^{''} + f_{1} y_{x}^{'} + f_{0} y = g(x) , f_{k} = f_{k} (x) $$
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