Wrong answer for ODE

MATLAB is giving the wrong answer to my ordinary differential equation.

m*diff(v) + p*v(t) == -g*m

The solution I am getting by solving it by hand is

C*exp(-(p*t)/m) - (g*m)/p

This is part of my code:

syms v(t) p m g
sol = dsolve (m*diff(v) + p*v(t) == -g*m)

sol = 

MATLAB says:

sol =

(C4*exp(-(p*t)/m) - g*m)/p

What am I doing wrong?

[Umer]

I just checked with 3 other places and their answers match with mine (by hand solution) but matlab can't be wrong, can it? i just wanna know if there's any coding error i made.

[Image Analyst]

How did you get the one you got by hand? Why is your exp() not divided by p? Is p a constant? If so then it could be bundled into the constant.

[Umer]

Oh yes!!! p IS a constant, that makes sense. sorry my bad. just learning this stuff for the first time. Thank youu so muchh.

Answer 1

[John D'Errico]

As is so often the case, a DIFFERENT answer is not always a WRONG answer. It may just look different. But different is not always a bad thing. (Why do I think these are words we all should take more seriously? Skipping the editorial comments...)

We can look at the ODE. You give no initial condition, but that should not be relevant. As well, you do not say which release of MATLAB you did that with.

syms m p g v(t)
ODE = m*diff(v) + p*v(t) == -g*m

ODE(t) = 

vsol = dsolve(ODE)

vsol = 

And that is the same as what you got from dsolve. But is it different? Remember that C1 in this solution is a COMPLETELY unknown parameter. As well, p is a CONSTANT, but it could be any constant.

So the only difference is that IF we decided to write

C = C1/p

then do you agree that the two solutions would now look the same?

[Umer]

Thank you so much!!