Error with simultaneous differential equations

Trying to solve:

"syms x(t) y(t) t

ode1 = diff(x,t,2)+2*x==y;

ode2 = diff(y,t,2)+2*y==x;

odes = [ode1; ode2]

cond1 = y(0)==2;

cond2 = x(0)==4;

cond3 = t(0)==0;

cond4 = diff(x,t)==0;

cond5 = diff(y,t)==0;

conds = [cond1; cond2; cond3; cond4; cond5]

[xSol(t), ySol(t)] = dsolve(odes, conds)"

BUT!

Array indices must be positive integers or logical values.

Error in indexing (line 1079)

R_tilde = builtin('subsref',L_tilde,Idx);

How to solve the error with y(0) and x(0) if it is initial condition for system of ODEs?

Answer 1

[Star Strider]

The problem is that ‘t’ is not a function (and shouldn’t be one), so ‘t(0)’ is interpreted as an array reference. Compounding that is that MATLAB subscript references are integers greater than 0, so that threw the error.

Assigning ‘Dx’ and the rest made referencing the derivatives easier, allowing this to now run without error —

syms x(t) y(t) t

Dx = diff(x);                               % Add These
D2x = diff(Dx);
Dy = diff(y);
D2y = diff(Dy);

ode1 = diff(x,t,2)+2*x==y;
ode2 = diff(y,t,2)+2*y==x;
odes = [ode1; ode2]

odes(t) = 

cond1 = y(0)==2; 
cond2 = x(0)==4;
% cond3 = t(0)==0;
cond4 = Dx(0)==0;
cond5 = Dy(0)==0;
% conds = [cond1; cond2; cond3; cond4; cond5]
conds = [cond1; cond2; cond4; cond5]

conds = 

[xSol(t), ySol(t)] = dsolve(odes, conds)

xSol(t) = 

ySol(t) = 

figure                                              % Just For Fun!
fplot(xSol, [0 10])
hold on
fplot(ySol, [0 10])
hold off
grid

EDIT — Fixed typos.

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[Denis]

Hello, Star Strider. You are the best, very thanks!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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