MATLAB ODE45: Why is there a big divergence between analytical and numerical solution?

Question

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?

red:analytical solution, blue: numerical

Answer 1

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')