@Preben Alsholm 

thanks...

@Preben Alsholm 

thanks...this system is similar to previous one.

yes i could  use the solution from that for an approximate solution

i dont know for this error!!

please check it, if possible for you

thanks...

@Preben Alsholm 

thanks alot Prof.Preben Alsholm ..

in another data i encounter with error

Error, (in dsolve/numeric/BVPSolve) unable to store '-HFloat(1.3406494995582793e11)+HFloat(73110.47081100458)*I' when datatype=float[8]

please help for remove it

thanks

DSOLVE3.mw

@tomleslie 

thanks...original my equations attached below.due to error ''

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system''''

for remove this error i added 

ode2 := diff(SYS[2], theta); SYS2 := {ode2, SYS[1], SYS[3]}

also by differential from SYS[2] i need to added three extra bc.thus  i added 

1-bcs22 := eval[recurse](convert(SYS[2], D), {theta = 1} union bcs2)

2-((D@@1)(h1))(0) = 0,

3-((D@@1)(h1))(1) = 0

please help me for gain answer

thanks

dsolve2.mw

@Carl Love 

yes we need eight boundary conditions but in original equations we need seven (7) BC,s  and i encounter with warning as

''unable to convert to an explicit first-order system"

how i can remove it

thanks...

warning-4.mw

Download warning-4.mw

@tomleslie 

omega is unknown!

i want determine it

@Carl Love 

thanks...but we need only one extra boundary conhition not two?

why approxsoln removed? i need  omega2, which they are possitive and 
 sorted in ascending order...

 also how determine amount b? this parameter is effective on result?

@tomleslie 

hello mr tomleslie 

is possible to pdsolve this equation with maple?

thanks..

@tomleslie 

thanks...

this boundary condition used in this paper that attached below.(EQS 8-10)

please see it

thanks..

Off-center_impact_of_an_elastic_column_by_a_rigid_mass.pdf

@tomleslie 

thanks..i upload it again and download it.this link is coreect

pde-bc-ic.mw

@tomleslie 

Thanks...

i Upload modified worksheet with new/corrected PDEs/BCS/ICS.

please see it

ICS..mw

@tomleslie 

thanks...i reform initial/boundary condition.only final initial condition decompose to two section.one of them is valid in domain x[0,La) and another is valid in x=La

please see attached file below

thanks..

PDE_reform.pdf

@tomleslie 

thanks...yes only PDE[1..3] are PDEs and PDE[a1..a3] are BC.(BOUNDARY CONDITION)

please see attached fie below

thanks...

PDE_are_as_following.pdf

@Kitonum 

i need obtaine one equation by substituting..... NOT at this format

@Preben Alsholm 

hi...if possible i need both Second and third branch...

thanks

result for third branch is as following figure