MATLAB: Do I get non-real solution for simple ODE

Question

Hello,

Following code:

syms a real
syms x(t)
assume(x(t), 'real')
ode = diff(x,t) == a*x;
odeSol = dsolve(ode);
isreal(odeSol)

The solution to this simple ode is, according to MATLAB, not real, since

isreal(odeSol)

results in 0. But the solution in reality is of course real.

The imaginary part:

imag(odeSol) = a*imag(exp(t))

Seems like t is not interpreted as real. Any suggestions why this happens?

I have also tried

syms t real

but that does not help either.

Thanks for your help!

Answer 1

syms a x0 real
syms x(t)
assume([x(t), t] , 'real')
ode = diff(x,t) == a*x;
odeSol = dsolve(ode, x(0)==x0);
 isreal(odeSol)