MATLAB: Solve the general solution of a Differential equation with boundary conditions

differential equationssolvesolve differential equation with boundary

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)

Best Answer

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

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MATLAB: Solve symbol four equations for c1 c2 c3 c4

Thanks, I solve it,

clc
clear
syms a b x y c1 c2 c3 c4 T1 T2 T3 T4  
T=c1+c2*x+c3*y+c4*x*y;
%%
r1=c1+c2*a+c3*b+c4*a*b-T1;
r2=c1-c2*a+c3*b-c4*a*b-T2;
r3=c1-c2*a-c3*b+c4*a*b-T3;
r4=c1+c2*a-c3*b-c4*a*b-T4;
%%Find C1 and C4
p13=r1+r3;
p24=r2+r4;
n1=solve(p13==0,c1);
n2=solve(p24==0,c1);
C4=solve(n1==n2,c4)
w1=solve(p13==0,c4);
w2=solve(p24==0,c4);
C1=solve(w1==w2,c1)
r1=subs(r1,c1,C1);
r1=subs(r1,c4,C4);
r2=subs(r2,c1,C1);
r2=subs(r2,c4,C4);
r3=subs(r3,c1,C1);
r3=subs(r3,c4,C4);
r4=subs(r4,c1,C1);
r4=subs(r4,c4,C4);
%%Find C3
q12=r1+r2;
q34=r3+r4;
C3=solve(q12==0,c3)
r1=subs(r1,c3,C3);
r2=subs(r2,c3,C3);
r3=subs(r3,c3,C3);
r4=subs(r4,c3,C3);
%% find C2
C2=solve(r1==0,c2)
r1=subs(r1,c2,C2);
r2=subs(r2,c2,C2);
r3=subs(r3,c2,C2);
r4=subs(r4,c2,C2);
C1
C2
C3
C4

MATLAB: Is the word “and” coming up in the output

Lucy, for example, in the expression for y5 there is a term

 cosh(p)*cosh(q)&cosh(t)

(typo?) which results in an and. The same (copy-paste?) happens in the other expressions, y6 thru y8.

Best Answer

Related Solutions

MATLAB: Solve symbol four equations for c1 c2 c3 c4

MATLAB: Is the word “and” coming up in the output

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