MATLAB: I want to solve the attached equation for “T”.

solve the equation

Please Help….

Best Answer

You assign values to all of the variables except for T__s and then you assign

Tfun = @(T__s)  (1/2) * (((C__r * (V__0^2 - 4*V__in^2) + 4 * V__0 * I__0 * T__s) / L__r)^(1/2) - (C__r * (V__0^2 - 4 * V__in^2) / L__r)^(1/2)) * L__r / V__in + (arcsin(2 * V__in / (V__0^2 + 4 * V__0 * I__0 * T__s / C__r)^(1/2)) + arcsin(V__0 / (V__0^2 + 4 * V__0 * I__0 * T__s / C__r)^(1/2))) / omega__r + 2 * (T__s * I__0 * L__r / V__0)^(1/2) + arccos(2 * V__in / V__0) / omega__r - T__s / 2;

after that you can

Ts_0 = rand()*50;    %some guess about the value
Ts_value = fzero(Tfun, Ts_0);

Related Solutions

MATLAB: Warning: Explicit integral could not be found

-(4/3) * (R12^4 * (B2^2 + A2^2) * A2 * (-(3/8) * exp(6 * B2 * L) + (-(3/16) * R12^4 + L * B2 * R12^2 + 3/8) * exp(2 * B2 * L) + (3/16) * R12^4 * exp(-2 * B2 * L)) * cos(2 * S12 + 2 * A2 * L) - (1/2) * R12^2 * (B2^2 + A2^2) * A2 * ((L * B2 * R12^2 + 1/8 - (3/8) * R12^4) * exp(4 * B2 * L) - (1/8) * exp(8 * B2 * L) + (3/8) * R12^4) * cos(4 * S12 + 4 * A2 * L) + (1/16) * R12^4 * A2 * (B2^2 + A2^2) * ( - exp(6 * B2 * L) + exp(2 * B2 * L)) * cos(6 * S12 + 6 * A2 * L) + (1/16) * B2 * (B2^2 + A2^2) * (R12^4 * exp(4 * B2 * L) + exp(8 * B2 * L)) * sin(2 * S12 + 4 * A2 * L) + (1/2) * R12 * B2^2 * A2 * ((R12^2 + 1/2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L)) * cos(3 * S12 + 2 * A2 * L) - (1/2) * ((R12^4 + R12^2) * exp(4 * B2 * L) + (1/2) * exp(8 * B2 * L)) * R12 * B2^2 * A2 * cos(4 * A2 * L + 3 * S12) + (1/2) * ((-R12^2 + 1/2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L)) * R12 * B2 * A2^2 * sin(3 * S12 + 2 * A2 * L) - (1/2) * R12 * ((R12^4 - R12^2) * exp(4 * B2 * L) + (1/2) * exp(8 * B2 * L)) * B2 * A2^2 * sin(4 * A2 * L + 3 * S12) + (1/16) * exp(6 * B2 * L) * B2 * R12^2 * (B2^2 + A2^2) * sin(4 * S12 + 2 * A2 * L) - (1/16) * exp(6 * B2 * L) * B2 * R12^2 * (B2^2 + A2^2) * sin(4 * S12 + 6 * A2 * L) - (1/4) * R12^3 * B2^2 * A2 * cos(5 * S12 + 4 * A2 * L) * exp(4 * B2 * L) + (1/4) * R12^3 * B2^2 * A2 * cos(6 * A2 * L + 5 * S12) * exp(6 * B2 * L) - (1/4) * R12^3 * A2^2 * B2 * sin(5 * S12 + 4 * A2 * L) * exp(4 * B2 * L) + (1/4) * R12^3 * A2^2 * B2 * sin(6 * A2 * L + 5 * S12) * exp(6 * B2 * L) + (1/4) * ((4 * R12^2 + 2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L) * (R12^2 + 3)) * R12 * B2^2 * A2 * cos(S12 + 2 * A2 * L) + (1/4) * ((4 * R12^2 - 2) * exp(6 * B2 * L) + R12^4 * exp(2 * B2 * L) * (-3 + R12^2)) * R12 * B2 * A2^2 * sin(S12 + 2 * A2 * L) - (1/2) * ((1/8) * R12^2 * B2 * (B2^2 + A2^2) * sin(2 * S12) + A2 * ((2 * R12 * B2^2 + (3/2) * B2^2 * R12^3) * cos(S12) - (3/2) * R12 * B2 * A2 * (R12^2 - 4/3) * sin(S12) + (B2^2 + A2^2) * (-(1/2) * R12^4 + 3/16 + L * B2 * R12^2))) * R12^2 * exp(4 * B2 * L) - (1/8) * sin(2 * A2 * L) * B2 * R12^2 * (B2^2 + A2^2) * exp(6 * B2 * L) + (-(1/16) * B2 * (B2^2 + A2^2) * sin(2 * S12) + (1/4) * (-2 * R12 * B2^2 * cos(S12) + 2 * A2 * R12 * sin(S12) * B2 + (B2 * L + (3/8) * R12^2) * (B2^2 + A2^2)) * A2) * exp(8 * B2 * L) - (1/4) * ((1/8) * R12^4 * (B2^2 + A2^2) * exp(-4 * B2 * L) + R12 * B2^2 * cos(S12) + A2 * R12 * sin(S12) * B2 + (L * B2 * R12^2 + 1 - (1/8) * R12^4) * (B2^2 + A2^2)) * R12^6 * A2) * R12^2 / ((R12^2 * (R12^8 * exp(2 * B2 * L) + 3 * R12^4 * exp(6 * B2 * L) + exp(10 * B2 * L)) * cos(2 * S12 + 2 * A2 * L) + (-R12^4 * exp(8 * B2 * L) - R12^8 * exp(4 * B2 * L)) * cos(4 * S12 + 4 * A2 * L) - (3/2) * R12^8 * exp(4 * B2 * L) - (1/6) * exp(12 * B2 * L) - (3/2) * R12^4 * exp(8 * B2 * L) - (1/6) * R12^12 + (1/3) * R12^6 * exp(6 * B2 * L) * cos(6 * S12 + 6 * A2 * L)) * B2 * (B2^2 + A2^2) * A2)

Note: If you substitute in the constants that you show, then the expression becomes very very sensitive to the exact value of L when you are near L = 0, especially in the slightly negative L range. This instability continues even if you do symbolic calculations with 256 digits precision.

MATLAB: How to solve differential equations in matrix form

    [vpexSol, vpeySol, vpezSol] = dsolve(eqn, C);
    vpexSol = simplify(vpexSol);
    vpeySol = simplify(vpeySol);
    vpezSol = simplify(vpezSol);

Best Answer

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MATLAB: Warning: Explicit integral could not be found

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