How can ı solve the differential equation this gives error, please help
c = 1.0;
b = 0.1;
σ = 0.01;
n = 1.0;
w1 = -(1/3) - (2 Sqrt[g[x]])/(3*c)*Cos[y]
w2 = -((b*b)/(g[x])^(n - 1))*(1 + σ)^n/(1 - g[x] + σ)
DSolve[g'[x] == -2*g[x]*(1 - g[x] + σ)*(w1 - w2) + σ*g[x]*(1 + 3*w1), g[x], x]
I do not know what your y there supposed to be (if it is a parameter, this is not a good name). If you use exact values, the errors go away. Since you are calling DSolve always try to avoid non-exact parameters in your ode.
ClearAll[x, y, g]
c = 1;
b = 1/10;
sigma = 1/100;
n = 1;
w1 = -(1/3) - (2 Sqrt[g[x]])/(3*c)*Cos[y]
w2 = -((b*b)/(g[x])^(n - 1))*(1 + sigma)^n/(1 - g[x] + sigma)
ode = g'[x] == -2*g[x]*(1 - g[x] + sigma)*(w1 - w2) + sigma*g[x]*(1 + 3*w1);
DSolve[ode, g[x], x]
The solution is implicit.
Update:
If initial conditions for g(x) is known, try NDSolve. For example:
ClearAll[x, y, g]
y = 20 Degree;
c = 1;
b = 1/10;
sigma = 1/100;
n = 1;
w1 = -(1/3) - (2 Sqrt[g[x]])/(3*c)*Cos[y]
w2 = -((b*b)/(g[x])^(n - 1))*(1 + sigma)^n/(1 - g[x] + sigma)
ode = g'[x] == -2*g[x]*(1 - g[x] + sigma)*(w1 - w2) + sigma*g[x]*(1 + 3*w1)
sol = NDSolve[{ode, g[0] == 1}, g, {x, 0, 1}]
To plot:
Plot[Evaluate[g[x] /. sol], {x, 0, 1}, PlotRange -> All]
20.0 and only use 20 to keep things exact. You can use the command Rationalize if needed. DSolve works better with exact numbers. (ofcourse, this also depends on what the ODE is, in your case, exact values removed those errors you were seeing).
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20 Degree, since your y is argument to Cos[] and I think you mean degrees. Second, the result is implicit. Which means, the solution g[x] is found by solving the resulting equation, which Mathematica could not solve exactly. i.e. This is the best M can do analytically. You could always try NDSolve ? Your ODE is non-linear in g(x) and so it is hard to solve these analytically.
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