How to simplify exponential symbolic equation?

I am solving a system of equations that have exponential terms in it. The equations are as follows:

x1_temp(t) == exp(-t*theta1_temp)*u1(t);

x2_temp(t) == exp(-t*theta2_temp)*(theta1_temp*x1_temp(t) + 19)

I want to ultimately find theta1 and theta2 from these equations. How can I isolate these variables and get an explicit equation? Using solve() or vpasolve() does not give answer. It gives an error saying that the input cannot be of type 'sym'.

Answer 1

[Birdman]

Something like this?

syms x1_temp(t) x2_temp(t) theta1_temp theta2_temp u1(t)
eq=[x1_temp(t)==exp(-t*theta1_temp)*u1(t) x2_temp(t) == exp(-t*theta2_temp)*(theta1_temp*x1_temp(t) + 19)];
solx=solve(eq,[theta1_temp,theta2_temp]);
theta1_temp(t)=solx.theta1_temp
theta2_temp(t)=solx.theta2_temp

[NUPUR THAKUR]

It returns empty sym.

[Birdman]

Actually it returns exactly the Torsten's answer. See the attached figure.

[NUPUR THAKUR]

Which version of MATLAB are you using?

[Birdman]

R2017b

[NUPUR THAKUR]

It worked. Thanks!

Answer 2

[Torsten]

theta1_temp(t)=-log(x1_temp(t)/u1(t))/t
theta2_temp(t)=-log(x2_temp(t)/(-log(x1_temp(t)/u1(t))/t*x1_temp(t)+19))/t

Best wishes

Torsten.