Su'(x)+v'(x)– 2u(x)– v(x)-1/x=0 -2и (х) — v'(х)+u(х)—v(х)—x* - 3х +1-0
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a) Determine the differential operators Ln , n = 1,2,3,4 and f(x), g(x) functions, which make it convenient to write the differential equation set in the first picture in the form given in the second picture.
b)Using the operators obtained above, obtain the differential equations provided by only the functions u(x) and v(x) through the elimination method.
c)Find the general solution of the system by solving the differential equations obtained in the previous part b) separately.
d)d) Write the homogeneous part of the differential equation system obtained in a) above, namely f(x)= g(x)=0 in normal form, and solve the resulting system using eigenvalues and eigen-
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