Strange behavior of dsolve

The results of these blocks of instructions are both correct but different:

syms r s K P0 P(t)
simplify(dsolve(diff(P,t) == r*P*(1-P/K)-s*P, P(0) == P0))
>> (K*P0*exp(t*(r - s))*(r - s))/(K*r - K*s - P0*r + P0*r*exp(t*(r - s)))

syms r g K P0 P(t)
simplify(dsolve(diff(P,t) == r*P*(1-P/K)-g*P, P(0) == P0)) 
>>  -(K*(g - r))/(r - (exp(t*(g - r))*(K*g - K*r + P0*r))/P0)

What's the matter with s and g???

My MATLAB version is 9.5.0.944444 (R2018b)

[Stephan]

interesting. same in R2019a.

Answer 1

[Stephan]

This workaround works in R2019a:

clear all
close all
clc
syms g r s K P0 P(t)
assume(g==s)
eq1 = simplify(dsolve(diff(P,t) == r*P*(1-P/K)-s*P, P(0) == P0))
eq2 = simplify(dsolve(diff(P,t) == r*P*(1-P/K)-g*P, P(0) == P0))
res = isequal(eq1,eq2)

Setting the assumption below the dsolve command will fail:

clear all
close all
clc
syms g r s K P0 P(t)
eq1 = simplify(dsolve(diff(P,t) == r*P*(1-P/K)-s*P, P(0) == P0))
eq2 = simplify(dsolve(diff(P,t) == r*P*(1-P/K)-g*P, P(0) == P0))
assume(g==s)
res = isequal(eq1,eq2)

Answer 2

[Víctor Jiménez López]

I've just discovered the "reason": alphabetical order (with respect to r)!!!! Symbolic variables like w, z produce the same result as s; variables like a, q produce the same result as g.

Weird stuff.