MATLAB: How to solve the coupled differential equation with variable coefficients

ode45

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.

Best Answer

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.
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