matlab solve not giving all the solutions

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mukesh bisht on 6 Nov 2021
Answered: Walter Roberson on 6 Nov 2021
Hi I have the following equation which has two solutions but the matalb "solve" giving only one solution. How can I get all the solutions for a equation?
syms x
eqn = (30.3760*exp(0.89*(pi-x))*cos(x))^2 + (2*2.6678 + 30.3760*exp(0.89*(pi-x))*sin(x))^2 == 2.1^2;
x = double(solve(eqn))
x = 4.7231;
But it has two solution (4.7231, 5.1110)

KSSV on 6 Nov 2021
Use vpasolve and specify the Intervel or initial condition. Read about vpasolve.
syms x
eqn = (30.3760*exp(0.89*(pi-x))*cos(x))^2 + (2*2.6678 + 30.3760*exp(0.89*(pi-x))*sin(x))^2 == 2.1^2;
r1 = vpasolve(eqn,4)
r1 =
4.7230742467055073214514048938575
r2 = vpasolve(eqn,5)
r2 =
5.1110533936277367834520435303963

Walter Roberson on 6 Nov 2021
The symbolic toolbox is not able to solve that to a closed form solution. It is a non-linear equation, and the symbolic toolbox is only able to find multiple solutions to polynomials (and certain cases where the non-linear equations happen to factor.)
format long g
syms x
Q = @(v) sym(v);
eqn = (Q(30.3760)*exp(Q(0.89)*(Q(pi)-x))*cos(x))^2 + (Q(2)*Q(2.6678) + Q(30.3760)*exp(Q(0.89)*(Q(pi)-x))*sin(x))^2 == Q(2.1)^2
eqn = Seqn = simplify(lhs(eqn)-rhs(eqn))
Seqn = string(Seqn)
ans = "(14417209*exp((89*pi)/50 - (89*x)/50))/15625 + (50648183*exp((89*pi)/100 - (89*x)/100)*sin(x))/156250 + 150366421/6250000"
fplot([Seqn, 0], [4.5 5.5]) sol = solve(Seqn)
Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.
sol =
4.7230742467055073214514048938575
sol1 = vpasolve(Seqn, 4.5)
sol1 =
4.7230742467055073214514048938575
sol2 = vpasolve(Seqn, 5.5)
sol2 =
5.1110533936277367834520435303963