# How can i solve this equation ?

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Mallouli Marwa on 18 Jan 2017
Hi
How ca i solve the attached equation to find lamda ?
When all the other terms are known.

If you want to get multiple answers use vpasolve function. Set the number of answers you want yo get and the code will pick some then in a random way.
syms lambda
Mt=1; % The value of your variables
m=1;
L=1;
lt=1;
eqn= 1+(cos(lambda)*cosh(lambda))+((lambda*Mt/(m*L))*(cos(lambda)*sinh(lambda)-sin(lambda)*cosh(lambda)))-((lt*lambda^3)/m*L^3)*(cosh(lambda)*sin(lambda)+sinh(lambda)*cos(lambda))+ ((Mt*lt*lambda^4)/m^2*L^4)*(1-cosh(lambda)*cos(lambda)) ==0;
for n = 1:50
vpasolve(eqn,lambda,'random',true)
end
this example gives you 50 answers. The answer before gives the first it finds.
syms lambda
Mt=1; % The value of your variables
m=1;
L=1;
lt=1;
eqn= 1+(cos(lambda)*cosh(lambda))+((lambda*Mt/(m*L))*(cos(lambda)*sinh(lambda)-sin(lambda)*cosh(lambda)))-((lt*lambda^3)/m*L^3)*(cosh(lambda)*sin(lambda)+sinh(lambda)*cos(lambda))+ ((Mt*lt*lambda^4)/m^2*L^4)*(1-cosh(lambda)*cos(lambda)) ==0;
k=zeros(1,50);
for n = 1:50
k(i)=vpasolve(eqn,lambda,'random',true)
end
that should create the vector

Just use the function solve, which uses numerical techniques to find variables.
try this.
syms lambda
Mt=1; % The value of your variables
m=1;
L=1;
lt=1;
%check if I wrote this correctly
eqn= 1+(cos(lambda)*cosh(lambda))+((lambda*Mt/(m*L))*(cos(lambda)*sinh(lambda)-sin(lambda)*cosh(lambda)))-((lt*lambda^3)/m*L^3)*(cosh(lambda)*sin(lambda)+sinh(lambda)*cos(lambda))+ ((Mt*lt*lambda^4)/m^2*L^4)*(1-cosh(lambda)*cos(lambda)) ==0;
value=solve(eqn,lambda) %solution for lamda
##### 2 CommentsShowHide 1 older comment
John D'Errico on 19 Jan 2017
You cannot find an infinite number of solutions. If you tried to write them all down, it would take infinitely long.

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