# Solve Differential Equation with initial conditions and function

2 views (last 30 days)
SamuLibero on 14 Mar 2023
Answered: Alan Stevens on 14 Mar 2023
Hello Everyone,
I have this differential equation: I have defined the function M(x) in the following way:
function M = Moment(x)
a = 800; %mm
b = 200; %mm
L = 1000; %mm
F = 1000; %N
if x<a
V = F*b/L;
M = V.*x;
elseif x >= a
M = F*a*(1-(x/L));
end
end
to solve the differential equation I've defined the following ode function based on previous ones:
xspan = 0:0.0002:1000;
y0 = [0 0];
[x,results] = ode45(@func3,xspan,y0);
function [dy] = func3(x,y)
E = 70000; %N/mm2
I = 32000; %mm4
y1 = y(1);
y2 = y(2);
dy1 = y2;
dy2 = -Moment(x)/(E*I);
dy = [dy1; dy2];
end
The main problem I'm trying to solve is that I have the boundary condition for the displacement y(0) = 0 and y(1000) = 0. I'm able to assign the first BD (i think), but i don't know how to assign the second one, since the solver refears to the function "Moment".

Alan Stevens on 14 Mar 2023
Try modifying your if statement in Moment. Something like
if x<a
V =...;
M = ...;
elseif x>=a && x<L
M = ...
else
M = 0;
end

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