Matlab: differential equation: starting conditions are wrong?

I solved manually: with

but if I solve it with Matlab:

syms v(t) g alpha  m v0; 

D = diff(v,t) == g - alpha/m*v; 

c1 = v;

cond = c1(0) == v0; 

S = dsolve(D,cond);

pretty(S)

I get a different solution, even if I'm sure mine is right.

I know this topic is a little vast, but maybe some of you talented people has time to investigate

Answer 1

[Cris LaPierre]

I'm no expert, but isn't the integral equal to

That way, the algebra works out to match the result MATLAB is giving you

syms v(t) g alpha  m v0; 
D = diff(v,t) == g - alpha/m*v; 
cond = v(0) == v0; 
S = dsolve(D,cond)

S = 

which simplifies to

[Cris LaPierre]

Here's more details on the derivation

Answer 2

[Walter Roberson]

syms v(t) g alpha  m v0; 
D = diff(v,t) == g - alpha/m*v; 
c1 = v;
cond = c1(0) == v0; 
S = dsolve(D,cond);

sum(cellfun(@(X) collect(X,[g,m,alpha]), children((collect(expand(S),g)))))

ans = 

[Niklas Kurz]

as always you're the master of formatation