# Slove function return empty solutions

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Roy on 16 Mar 2023
Commented: Walter Roberson on 24 Mar 2023
Hello, I'm trying to solve the attached syntax, but the aolve function return empty solutions. Please help.
syms V_1 V_2 x_1 x_2 r
pi1 = (V_1) * (x_1^r/(x_1^r+x_2^r)) - x_1
pi2 = (V_2) * (x_2^r/(x_1^r+x_2^r)) - x_2
dpi1dx = diff(pi1, x_1)
dpi2dx = diff(pi2, x_2)
s = solve(dpi1dx==0, dpi2dx==0, x_1, x_2)
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Walter Roberson on 24 Mar 2023
I am very busy these days.

Walter Roberson on 16 Mar 2023
Use dsolve for differential equations
Roy on 21 Mar 2023
noway :(
this is the solution for general r and V_1 != V_2
x_1 = V_2*(r*(V_2/V_1)^(r-1))/(1+(V_2/V_1)^r)^2
x_2 = V_1*(r*(V_1/V_2)^(r-1))/(1+(V_1/V_2)^r)^2
placing x_1 and x_2 and the dpi1dx and dpi2dx become them to 0.

Roy on 21 Mar 2023
Why MATLAB can't solve this simple equations?
the solution for general r and V_1 != V_2:
x_1 = V_2*(r*(V_2/V_1)^(r-1))/(1+(V_2/V_1)^r)^2
x_2 = V_1*(r*(V_1/V_2)^(r-1))/(1+(V_1/V_2)^r)^2
placing x_1 and x_2 and the dpi1dx and dpi2dx become them to 0.
Roy on 22 Mar 2023
Edited: Roy on 22 Mar 2023
So why MATLAB can't solve it, and extract these x_1 and x_2 when dpi1dx=0 and dpi2dx=0 using solve() or something else?
Btw, all the varibles are positive
There is solution for this simple equations :(
x_1 = V_2*(r*(V_2/V_1)^(r-1))/(1+(V_2/V_1)^r)^2 x_2 = V_1*(r*(V_1/V_2)^(r-1))/(1+(V_1/V_2)^r)^2

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