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can anyone help me to solve this equation ?. is this equation linear or not?

knowing, this equation represents the equation of motion for frame members for materials which have different moduli in tension and compression (civil engineering).

"EI" ("x,t" ) ("∂" ^"4" "u" ("x,t" ))/〖"∂x" 〗^"4" "-N" ("x" ) ("∂" ^"2" "u" ("x,t" ))/〖"∂x" 〗^"2" "+m" ("x,t" ) ("∂" ^"2" "u" ("x,t" ))/〖"∂t" 〗^"2" "=0"

In which,

EI depends on a roots of cubic equation, and t depends on ("∂" ^"2" "u" )/〖"∂t" 〗^"2" (acceleration)

boundary conditions:

at x=0, u=0 and at x=L, u=0

at t=0, u=0

knowing, this equation represents the equation of motion for frame members for materials which have different moduli in tension and compression (civil engineering).

"EI" ("x,t" ) ("∂" ^"4" "u" ("x,t" ))/〖"∂x" 〗^"4" "-N" ("x" ) ("∂" ^"2" "u" ("x,t" ))/〖"∂x" 〗^"2" "+m" ("x,t" ) ("∂" ^"2" "u" ("x,t" ))/〖"∂t" 〗^"2" "=0"

In which,

EI depends on a roots of cubic equation, and t depends on ("∂" ^"2" "u" )/〖"∂t" 〗^"2" (acceleration)

boundary conditions:

at x=0, u=0 and at x=L, u=0

at t=0, u=0

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