# How to solve this complicated equation

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AJMIT KUMAR on 19 Jan 2021
Commented: AJMIT KUMAR on 22 Jan 2021
Find the value of D ? (In RHS term, D is also present, see equations below) where
(Note - Use N(x,t) instead of N(z,t)) where Additional equations are:- (If required then use only) ;(I haven't used these in my calculation)  I have tried this code but getting error that Symbolic parameters not supported in nonpolynomial equations if I use "vpasolve" command; and getting Warning: Unable to find explicit solution, if I use "solve" command : -
( I have denoted "ri+" as y; "ri-" as z ; "gamma" as g ; "beta" as b ; "N_infinity" as u ; "n_infinity" as v ; "Sigma" as O ; "delta" as d ; "i" as s ; )
clear all; clc;
syms x d y z t s D h g b u v
K = (pi*pi*D)/(h^2);
y = 0.5*((K*s*s + g + b)+ sqrt(((K*s*s + g + b)^2) - 4*K*b*s*s));
z = 0.5*((K*s*s + g + b)- sqrt(((K*s*s + g + b)^2) - 4*K*b*s*s));
F = symsum(((-1)^(0.5*(s-1)))*(cos(0.5*pi*s*x/d))*((y*exp(z*t)-z*exp(y*t))/(s*(y-z))),s,1,Inf);
N = (g*v/b)*((1 - 4/pi)*F);
F1 = diff(N,t);
G = symsum(((-1)^(0.5*(s-1)))*(cos(0.5*pi*s*x/d))*(y*z)*((exp(z*t)-exp(y*t))/(s*(y-z))),s,1,Inf);
n = v*(((1 - 4/pi)*F) + ((4/(pi*b))*G));
G1 = diff(n,t);
G2 = diff(n,x,2);
eqn = [D*(G2) == (G1)+ (F1)*(F1)];
eqn = rewrite(eqn,'log'); % Additional step
[R] = vpasolve(eqn,D);
AJMIT KUMAR on 19 Jan 2021
If you need other information, feel free to ask

amin on 20 Jan 2021
Hi Ajmit,
It is not an easy one!
1) mistake in parantheses in 'n' and 'N'. They should be:
N = (g*v/b)*(1 - 4*F/pi);
n = v*(1 - 4*F/pi + 4*G/(pi*b));
3) In all series, you have to consider only odd values of i (i=1,3,5,...,inf). So, in the code, you sould replace all 's' by '2*s-1'.
Correcting all these issues, 'solve' function could not solve the eqn and it returns the same warning that you received, which means that Matlab cannot find a closed form explicit solution.
I recommend you to double check for more possible mistakes and then you may try 'ode'.
Hope it helps!
good luck
AJMIT KUMAR on 22 Jan 2021
@amin Thankyou for pointing out correction and I found the numerical value of many terms here, finally equation solved

R2019a

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