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# Can dsolve is enough to solve these ODEs

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MINATI PATRA on 18 Nov 2020
Closed: MATLAB Answer Bot on 20 Aug 2021
syms a s t y u(y,t) g(y,t) h(y,t) M Kp Pr phi Gr Gc Sc Kc U(y,s) T(y,s) C(y,s)
% % Gr = 1; Gc = 1; M =1; Kp = 0.1; Pr = 1; phi = 0.1; Sc = 0.22; Kc = 1;
xa = 0; xb = 5;
E1 = laplace( diff(u,t) - diff(u,y,2) + (M+Kp) * u(y,t) - Gr * g(y,t) - Gc * h(y,t) );
E2 = laplace( diff(g,t) - (1/Pr) * diff(g,y,2) + phi * g(y,t) ); E3 = laplace( diff(h,t) - (1/Sc) * diff(h,y,2) + Kc * h(y,t) );
E = simplify( [E1, E2, E3] ); EI = subs( E,[u(y, 0), g(y, 0), h(y, 0)], [0 0 0] ); %% IC
EEL = subs(EI, [ laplace(u(y, t), t, s),laplace(diff(u(y, t), y, y),t,s), ...
laplace(g(y, t), t, s), laplace(diff(g(y, t), y, 2), t, s),...
laplace(h(y, t), t, s), laplace(diff(h(y, t), y, 2), t, s) ], ...
[U(y,s), diff(U(y,s),y,2), T(y,s),diff(T(y,s),y,2), C(y,s), diff(C(y,s),y,2)]);
%% Boundary Conditions
Cond = [U(xa,s) == a/s^2, T(xa,s) == 1/s^2, C(xa,s) == 1/(s-1), U(xb,s) == 0, T(xb,s) == 0, C(xb,s) == 0];
%%% HERE I have done something wrong
S = dsolve( EEL == [0 0 0],Cond)
%% I want symbolic expression of U, T, C in terms of y and s