i want mathlab programme for solving linear differential equation as metioned below

dx1/dt= k3*x3-k1*x1+ 10, dx2/dt= k1*x1-k2*x2, dx3/dt= k2*x2-k3*x3

Answer 1

[Dyuman Joshi]

syms x1(t) x2(t) x3(t) k1 k2 k3

ode1 = diff(x1)==k3*x3-k1*x1+10;
ode2 = diff(x2)==k1*x1-k2*x2;
ode3 = diff(x3)==k2*x2-k3*x3;

dsolve([ode1 ode2 ode3])

ans = struct with fields:
    x2: (k3*(C1 + (10*k1*k2*t)/(k1*k2 + k1*k3 + k2*k3)))/k2 - exp(-(t*(k1 + k2 + k3 - (k1^2 - 2*k1*k2 - 2*k1*k3 + k2^2 - 2*k2*k3 + k3^2)^(1/2)))/2)*(C3 + (exp((k1*t)/2 + (k2*t)/2 + (k3*t)/2 - (t*(k1^2 - 2*k1*k2 - 2*k1*k3 + k2^2 - 2*k2*k3 + k3^2)^(1/2)…
    x1: exp(-(t*(k1 + k2 + k3 + (k1^2 - 2*k1*k2 - 2*k1*k3 + k2^2 - 2*k2*k3 + k3^2)^(1/2)))/2)*(C2 + (exp((k1*t)/2 + (k2*t)/2 + (k3*t)/2 + (t*(k1^2 - 2*k1*k2 - 2*k1*k3 + k2^2 - 2*k2*k3 + k3^2)^(1/2))/2)*((10*k1*k2^2 + 10*k1^2*k2 + 10*k1*k2*k3 + 10*k1*k…
    x3: C1 + exp(-(t*(k1 + k2 + k3 - (k1^2 - 2*k1*k2 - 2*k1*k3 + k2^2 - 2*k2*k3 + k3^2)^(1/2)))/2)*(C3 + (exp((k1*t)/2 + (k2*t)/2 + (k3*t)/2 - (t*(k1^2 - 2*k1*k2 - 2*k1*k3 + k2^2 - 2*k2*k3 + k3^2)^(1/2))/2)*(10*k1*k2 - (10*k1*k2^2 + 10*k1^2*k2 + 10*k1…