Solving matrix differential equation

Hi I want to solve a 2x2 matrix differential equation, how do I go by it?

this is what i currently have

syms x1 x2
Dx1 = diff(x1);
Dx2 = diff(x2);
A = [22.2 -6.2; -9.8 9.8];
ode = diff(x1,x2,2) == A*[x1;x2]

ode = 

cond1 = x1(0) == 0;

Array indices must be positive integers or logical values.

Error in indexing (line 956)
R_tilde = builtin('subsref',L_tilde,Idx);

cond2 = Dx1(0) == 0;
cond3 = x2(0) == 1;
cond4 = Dx2(0) == 0;
conds = [cond1 cond2 cond3 cond4];
ySol(t) = dsolve(ode,conds);
ySol = simplify(ySol);

A is a matrix [22.2 -6.2; -9.8 9.8]

Answer 1

[Walter Roberson]

You try to take the derivative of x1 with respect to x2. You cannot meaningfully take the derivative of a function with respect to a different function.

If you try to define x1 as a function of x2 then you are going to end up with a function of more than one variable, which would be a PDE rather than an ODE.

syms x1(t) x2(t)
Dx1 = diff(x1);
Dx2 = diff(x2);
A = [22.2 -6.2; -9.8 9.8];
ode = diff(x1,x2,2) == A*[x1;x2]

ode(t) = 

cond1 = x1(0) == 0;
cond2 = Dx1(0) == 0;
cond3 = x2(0) == 1;
cond4 = Dx2(0) == 0;
conds = [cond1 cond2 cond3 cond4];
ySol = dsolve(ode,conds)

ySol = struct with fields:
    x2: 0
    x1: 0

[Walter Roberson]

Guessing at what you really want:

syms x1(t) x2(t)
Dx1 = diff(x1);
Dx2 = diff(x2);
A = [22.2 -6.2; -9.8 9.8];
ode = diff([x1;x2],2) == A*[x1;x2]

ode(t) = 

cond1 = x1(0) == 0;
cond2 = Dx1(0) == 0;
cond3 = x2(0) == 1;
cond4 = Dx2(0) == 0;
conds = [cond1 cond2 cond3 cond4];
ySol = dsolve(ode, conds)

ySol = struct with fields:
    x2: exp(-t*(16 - (4*155^(1/2))/5)^(1/2))*((10*(16 - (4*155^(1/2))/5)^(1/2))/49 - (5*(16 - (4*155^(1/2))/5)^(3/2))/784)*((155^(1/2)*(16 - (4*155^(1/2))/5)^(1/2))/80 - (155^(...
    x1: exp(-t*(16 - (4*155^(1/2))/5)^(1/2))*((5*(16 - (4*155^(1/2))/5)^(1/2))/49 - (5*(16 - (4*155^(1/2))/5)^(3/2))/784)*((155^(1/2)*(16 - (4*155^(1/2))/5)^(1/2))/80 - (155^(1...

ySol = simplify([ySol.x1; ySol.x2])

ySol = 

[Ibraheem]

Thanks