dsolve unable to find a solution

Hi, I need to find a solution for the differential equation (image attached), where theta, gamma and M are parameters. I am trying to solve the equations using dsolve (code attached). It returns an error "Warning: Unable to find explicit solution." Am I doing something wrong or should I use a different ode solver for this equation? Please help! Thanks!

Answer 1

[Sam K]

Sorry about the confusion about the notation. The superscript "T" in my model is not the transpose. The notation denotes the type of source in my model, which is irrelevant to my question here. So, please ignore the superscript "T".

[Walter Roberson]

In any case you have QT multiplied by something in the image but evaluated at something instead of multiplied in the code.

[Walter Roberson]

>> syms theta lambda M
>>  a = (1 - theta/exp(lambda*M));
>> syms Q(t)
>> eqn = diff(Q,t) == Q*a;
cond = Q(0) == 400;
qSol(t) = dsolve(eqn,cond)
qSol(t) =
400*exp(-t*exp(-M*lambda)*(theta - exp(M*lambda)))

Answer 2

[Walter Roberson]

Your image shows Q transpose multiplied by something, but your function has Q evaluated at something not multiplied.

Answer 3

[Sam K]

Hi walter,

Thank you for helping me out with this. I see your point. I guess that is part of my confusion on how to write the code. My equation for Q, as shown in the picture, is: dQ/dt = Q*a, where a is the parameters in the parentheses. I need to plot this equation based on the initial value of Q. I thought dsolve would be a good solver, but I must be doing something wrong with the code since I am a newbie to Matlab coding. Should I change the code as follows:

 a = (1 - theta/exp(lambda*M));
syms Q(t) a
eqn = diff(Q,t) == Q*a;
cond = Q(0) == 400;
qSol(t) = dsolve(eqn,cond);