Solve the general solution of a Differential equation with boundary conditions

Hi

I have the general solution of a differential equation and the boundary conditions. How can I solve this?

w(x)=C1+C2*x+C3*(x^2)+C4*(x^3)+(L^4)*C5*cosh(x/L)+(L^4)*C6*sinh(x/L)

w(0)=0

w'(0)=0

w''(0)=0

w''(L)=0

w'''(L)-(L^2)*w'''''(L)=F/(E*I)

w''(L)-(L^2)*w''''(L)

Answer 1

[Torsten]

Tell the program which gave you the general solution to additionally incorporate the six boundary conditions.

[Vlasis Demosthenes]

I don't have the exact differential equation from which the general solution emerged.

Is there any way to solve this? from the general solution and the boundary conditions only?

[Torsten]

Build w', w'', w''' and w'''' of w and evaluate the conditions. You'll arrive at a linear system of equations in the Ci's as unknowns.

I'll do it for the first two conditions:

w(0)=0 leads to

C1+C2*0+C3*(0^2)+C4*(0^3)+(L^4)*C5*cosh(0/L)+(L^4)*C6*sinh(0/L) = 0, thus

C1 + L^4*C5 = 0

w'(0)=0 leads to

C2+2*C3*0+3*C4*(0^2)+(L^4)/L*C5*sinh(0/L)+(L^4)/L*C6*cosh(0/L) = 0, thus

C2 + L^3*C6 = 0

...

Once you have the equations, write them as a system of linear equations in the form A*C = b with a 6x6 matrix A and a 6x1 vector b.

Then C is given by

C=A\b

Best wishes

Torsten.