Hello guys

I have a coupled linear differentional equation which are in the 4th order. they are shown in the below:

P:=phi(x):
Q:=psi(x):

eq1:=a11*diff(P,x,x,x,x)+a22*diff(P,x,x)+a33*P+a44*diff(Q,x,x)+a55*Q:
eq2:=a44*diff(P,x,x)+a55*P+a66*diff(Q,x,x)+a77*Q:

eq1:=0:
eq2:=0:

The boundary values for this coupled equation are:
phi(a)=sigma1,phi(-a)=sigma1,diff(P,x)(a)=0,diff(P,x)(-a)=0,psi(a)=sigma2,psi(-a)=sigma2

Now consider:

a11:=6.36463*10^(-10):
a22:=-1.22734*10^(-9):
a33:=3.48604*10^(-10):
a44:=2.94881*10^(-11):
a55:=-5.24135*10^(-11):
a66:=-1.03829*10^(-9):
a77:=4.86344*10^(-10):
when I use dsolve for deriving a good answer in this equation, there are six real roots .How can I solve it with these boundary condition?

I need to extract phi(x) and psi(x) from this coupled equation.

Thanks

Hello guys

I have a linear differentional equation which is in the 4th order. It is shown in the below:

P:=phi(x):
eq:=a11*diff(p,x,x,x,x)+a22*diff(p,x,x)+a33*p:
eq:=0:
where a11 and a22 and a33 are constant coefficients. The boundary value for this equation is:

phi(a)=sigma1 , phi(-a)=sigma1 , diff(p,x)(a)=0 , diff(p,x)=0

Now consider :

a11:=2.731e-10:
a22:=-1.651e-9:
a33:=3.09027e-10:
a:=35.714:
sigma1:=200e6:

when I use dsolve for deriving a good answer in this equation. there are four real roots .How can I solve it with these boundary condition?

I need to extract phi(x) from this equation.

Thanks

I have a characteristic equation. some times It has polar roots . sometimes It has real roots and sometimes both of them.

I want to extract real roots and extract polar roots if they are.

for instance:

q:=m3*r^3+m2*r^2+m1*r+m0:

rot:=solve(q=0,r);

I want to know how can I use if in this part ?

Hello guys

I have a question:

I have an equation like below. Always it has different order for example :

T1:=q3*(r^6)+q2*(r^4)+q1*(r^2)+q0:
solve(T1=0,r):
and sometimes:

T2:=q5*(r^4)+q6*(r^2)+q7:
solve(T2=0,r):
q0,q1,q2,q3,q4,q5,q6 and q7 are constants.

We know that for T1 It has two real answer and for T2 we have any real answer.

How can I specify generally the real answers for all of them?

I want to use these real answer for another equation.

Thanks

I have an expression like this:
B0:=(phi(x))^2:
B1:=diff(phi(x),x):
B2:=diff(phi(x),x,x):
B3:=B2^2:
B4:=(phi(x))^2:
B5:=B1^2:

C0:=(psi(x))^2:
C1:=diff(psi(x),x):
C2:=:C1^2:
C3:=

D0:=(eta(x))^2:

F1:=phi(x)*psi(x):
F2:=phi(x)*eta(x):
F3:=psi(x)*eta(x):

g1:=B1*C1:
g2:=B2*phi(x):
g3:=B2*psi(x):
g4:=B2*eta(x):

T:=A0011*B0+A0022*C0+A0033*D0+A0012*F1+A0013*F2+A0023*F3+A1111*B5+A1122*C2+A1112*g1+A2011*g2+A2012*g3+A2013*g4+A2211*B5:

A0011 and A0022 and etc are constants and coefficients.

Now I want to extract some constants like A1112 or A2013 from T. Please write out an useful code for extract these coefficients!

Thanks