# ode with varying constant

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prajyot gajbhiye on 21 Oct 2020
Answered: Star Strider on 21 Oct 2020
i have one differntial eqation and in that i have two constants one is scalar and one is vector i have to solve diffential equation for each value of vector means i got no of diff equation= no of elements in vector now i have to plot each solution of each de with time
function [dydt] = diffvar(t,y)
dydt=-k*y+a;
end

Ameer Hamza on 21 Oct 2020
prajyot gajbhiye on 21 Oct 2020
but you have considered both as scalar
Ameer Hamza on 21 Oct 2020
That code will work even if you put one of the variable as scalar.

Star Strider on 21 Oct 2020
Interpolating a time-domain vector in a differential equation is essentially described in the ode45 (and other solvers) documentation. This simply re-states it in the context of the current problem.
Try this
ic = 0;
tspan = [0 10];
k = 42;
av = rand(1,10); % Vector Defining ‘a’
a = @(t) interp1(linspace(min(tspan),max(tspan),numel(av)), av, t); % Function Interpolating ‘a’
[T,Y] = ode45(@(t,y)diffvar(t,y,k), tspan, ic);
figure
plot(T, Y)
grid
function [dydt] = diffvar(t,y,k)
dydt=-k*y+a(t); % Call ‘a’ As A Function
end
Use your own vector for ‘av’ and your own constant for ‘k’.