if we use backward euler's method to solve following differential equation , for which values of h the method is convergent?
$y^{\prime}(t)=\lambda y(t)+g(t), \quad y\left(t_{0}\right)=y_{0}, \quad \lambda<0$
assume values of |$\lambda$| is big.
I tried to solve equation
$y^{\prime}(t)-\lambda y(t)=g(t)$
Where the above equation is linear we have
$y(t)=e^{\lambda t}\left[\int_{0}^{t} g(x) d x+C\right]$ Now I don’t know how I can find values of h that $\lim _{n \rightarrow \infty} e_{n, h}=0$