How to solve ODE's and find m(t) using matlab? Urgent!!

Here is the given ODE for which I need a solution:

Please help me on how to do this!!!

[Ben11]

Do you have the Symbolic Math Toolbox?

[Shubham Maurya]

No, where it is?

Answer 1

[Star Strider]

Use ode45. It’s five lines of code, including the plot:

mdot = @(t,m) sqrt(2E+5.*((1+(0.4-m)./0.5).^-1.4 - 1));
[t,m] = ode45(mdot, [0 1], 0.001);
figure(1)
semilogy(t, real(m), '-b',  t, imag(m), '-g')
grid

[Shubham Maurya]

Can you explain the syntax of ode45(). I mean what is [0,1] and 0.001

[Shubham Maurya]

My initial value is m(0)=0.4, and domain of t is [0,0.5]

[Star Strider]

Since I did’t have other information, I chose m(0)=0.001 and ran it from [0 1] in time. With your m(0)=0.4 and time span [0 0.5] the call to ode45 is:

[t,m] = ode45(mdot, [0 0.5], 0.4);

and the entire code is now:

mdot = @(t,m) sqrt(2E+5.*((1+(0.4-m)./0.5).^-1.4 - 1));
[t,m] = ode45(mdot, [0 0.5], 0.4);
figure(1)
plot(t, m, '-*b')
grid
axis([xlim    0  0.5])

With the square root, I’m somewhat surprised that there aren’t two solutions, for instance ±0.4 but the routine produces only one. Yours is a nonlinear equation, and the Symbolic Math Toolbox cannot solve it. (I have it, and I tried that to see what it would do. There is no analytic solution.)

The output doesn’t change from the initial conditions, and is uniformly 0.4 from 0 to 0.5.