How can I solve the coupled differential equation with variable coefficients?

I try to solve coupled differential equation in matlab. This is the code I was typed in matlab

syms u(t) v(t)
ode1 = diff(u) == v;
ode2 = diff(v) == ((5/sqrt(2))*exp((1-sqrt(2))*t)-(5/sqrt(2))*exp((1+sqrt(2))*t)+1)*u + (((5*(1-sqrt(2)))/sqrt(2))*exp((1-sqrt(2))*t)-((5*(1+sqrt(2)))/sqrt(2))*exp((1+sqrt(2))*t)+2)*v;
odes = [ode1; ode2]
cond1 = u(0) == 1;
cond2 = v(0) == 0;
conds = [cond1; cond2];
[uSol(t), vSol(t)] = dsolve(odes,conds)

In command window

Warning: Unable to find explicit solution. 
> In dsolve (line 190)
  In coupled (line 8) 
Error using sym/subsindex (line 855)
Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic variables, and function body must be sym expression.

Error in coupled (line 8)
[uSol(t), vSol(t)] = dsolve(odes,conds)
 

Can someone help me with this error? Thank you.

[David Goodmanson]

Hi VMRS,

CORRECTED:

If you change the last line to

[uSol vSol] = dsolve(odes,conds)

then you get no errors, just

Warning: Unable to find explicit solution. 
> In dsolve (line 190)
  

which is not really surprising.

[Vellapandi M Research Scholar]

Thank you for your response. But I get the same error. I am confused. What is the mistake in the last line?

[David Goodmanson]

sorry, I copied in the wrong line. See correction above.

[Vellapandi M Research Scholar]

Thank you once again. I need solution in terms of t. But I get this.

Warning: Unable to find explicit solution.

> In dsolve (line 190)

In coupled (line 8)

uSol =

[ empty sym ]

vSol =

[ ]

[David Goodmanson]

that's right. Matlab can't solve it symbolically, but there is always numerically..

Answer 1

[Dinesh Yadav]

Hi Vellapandi,

Continuing from David Goodmanson's comment you can solve it numerically. Below is the code for it.

tspan = [0 5];
y0=[1;0];
[uSol, vSol] = ode45(@(t,x) [x(1);((5/sqrt(2))*exp((1-sqrt(2))*t)-(5/sqrt(2))*exp((1+sqrt(2))*t)+1)*x(2) + (((5*(1-sqrt(2)))/sqrt(2))*exp((1-sqrt(2))*t)-((5*(1+sqrt(2)))/sqrt(2))*exp((1+sqrt(2))*t)+2)*x(1)],tspan,y0)

You can change the time limits as per your application.

You can refer to documentation link below to see how to solve system of differential equations.

https://www.mathworks.com/matlabcentral/answers/384186-how-to-solve-two-differential-equations-using-ode45

Hope it helps.