I get the feeling I'm making a mistake somewhere here since the error is extremely high

Compute by hand using the Euler Method given:

Problem:

$\displaystyle y' = -100y+1 $

$\displaystyle y(0)=1$

Attempt:

Euler Method: y_{i+1}= y_{i}+ h*f(t_{i},y_{i}) where h is the arbitrary step size which in this case will be 0.1

y_{i}= 0

h = 0.1

f(t_{i},y_{i}) = f(0,1) = -100(1) + 1 = -99

y_{i+1}= 1 + (-99)(0.1) = -8.9

To calculate percent error, find the exact solution.

Solving the ODE yields:

y = 1/100 + 99/(100*e^{100t})

Plugging in 0.1 for t yields approximately 0.01005 for the exact solution as opposed to -8.9 in the approximated solution