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I am studying Partial DE for my Master's. I face a lot of difficulties in understanding them. It is the first time I am studying in my academic studies. My main goal is to understand when systems are …

I have this system. I have found the equilibrium points and the Jacobian Matrix of each point. Now I am trying to calculate the eigenvalues and in the second step solve numerical the system. r = 1; b …

I am trying to determine the equilibrium points r=1; b=1; c=0.01; μ=0.4; deq1 = x'[t] == r*x[t] - b*x[t]^2 - c*x[t]*y[t] - 0.75*x[t]*y[t]/(a + x[t]) deq2 = y'[t] == μ*y[t] + 0.75*x[t]*y[t]/(a + x[t]) …

It is given the following problem: $$x'=rx-bx^2-cxy-\frac{\beta xy}{\alpha+x}$$ $$y'=-\mu y+\frac{\beta xy}{\alpha+x}$$ With parameters $r=1,b=1,c=0.01, \mu=0.4,\alpha= 0.36$ and initial values $x(0)= …

It is given the following problem: $$X'=Z+(Y-\alpha)X$$ $$Y'=1-\beta Y-X^2$$ $$Z'=-X-\gamma Z$$ with initial conditions $(X(0),Y(0),Z(0)=(1,2,3)$. Where X: interest rate Υ:investment demand Z: price i …

I am trying to solve the following problem. I have the following constants and the differential equations. r=1; b=1; c=0.01; a=0.36; a1=0.01; a2=0.05; c1=2; c2=1; μ=0.4; m=0.01; d=0.5; e=15; deq1 = x …

I tried to simulate the Lorenz83 Attractor that is defined by the following system of nonlinear ordinary differential equations: \begin{eqnarray*} \frac{dx}{dt}&=&-a x - y^2 - …

Merry Christmas to all. We have a problem we want to breed rainbowfish to sell to pet stores. We start with a nice big aquarium and 30 fish, half of them male, half of them female. We want to predict …

The mathematical model is $$V'=\frac{I}{C}, V(0)=0$$ and $$I'=\frac{-V}{L}-\frac{RI}{L}+\frac{V_β}{L}, I(0)=0$$ With I.C $V_β=5 V, R=0.1Ω, L=4*10^{-9}H and C=0.5*10^{-9}F $ I have calculated and I hav …

I want to use appropriately use the Manipulate command in conjunction with Plot, to construct animated graphics for the evolution of the solution. I have tried but i could not succed to solve it $f(x) …

Given the analytical solution f[x_] := Exp[-x^2/2] (1 + 0.2*HermiteH[4, x] + 0.01*HermiteH[6, x]) n = 10; A = Table[ 1/(Sqrt[Pi] 2^m m!) Integrate[ f[x] HermiteH[m, x] Exp[x^2/2], {x, 0, 1}], …

soln = DSolve[y''[x] + y'[x] + y[x] == 0, y[x], x] solTable = Table[soln /. {C[1] -> i, C[2] -> j}, {i, -1, 1, 1}, {j, -1, 1, 1}] Plot[solTable, {x, -2, 4}] I am trying to generate the plot of the …

I am trying to solve the following differential equation $$p'(t)=0.7p(t)(1-\frac{p(t)}{750})-20$$ and has an initial value $p(0)=30$ eqn = p'[t] == 0.7 p[t]*(1 - p[t]/750) - 20 sol = DSolve[{eqn, p[0] …

We study the paper "Dynamic analysis and control of a new hyperchaotic finance system" It is given the following system $$X'=Z+(Y-\alpha)X$$ $$Y'=1-\beta Y-X^2$$ $$Z'=-X-\gamma Z$$ with initial condit …

Given the following problem $$u_{t}-\frac{v}{2}\cdot u_{xx}+\frac{v}{2}\cdot x^2 \cdot u(x)=0 $$ $$u(x,0)=f(x)$$ Where $ f(x)=y_1(x)+0.2y_4(x)+0.01y_6 (x) $ $y_n$ are the Eigenfunctions that defined …