at the moment I try to understand ode45. So I would like to solve an exercise. The differential equation is: y=y' with y(0)=10. I wrote this code:
tspan = [0 5];
y0 = 10;
[t,y] = ode45(@(t,y) y, tspan, y0);
plot(t,y);
I know that the analytical solution would be the exponential-function. So I inserted it in the plot to verify the solution. (The exp function needs to be shifted by 9 upwards.)
hold on;
fplot(@(x) exp(x)+9,tspan,'r')
But there is a divergence I cannot explain. What I've understand wrong?
The true solution of this diffential equation with this initial condition is : 10*exp(t)
for y'(t) = y(t)
the solution is of the form c.exp(t) with c a constant.
Using the initial condition : y0 = 10
We have : c exp(0) = 10
therefore c = 10;
Therefore you are not comparing the correct amount,
Use : fplot(@(x) 10*exp(x),tspan,'r')
