I have the following system:
$$f(t) = t \cdot f(t) + g(t)$$ $$g'(t) = g(t) + t \cdot g'(t) + f(t)$$
which I want to solve for $f(t)$ and $g(t)$. I also have initial conditions that $f(0)=g(0)=1$. How do I go about this in the best way?
I have the following system:
$$f(t) = t \cdot f(t) + g(t)$$ $$g'(t) = g(t) + t \cdot g'(t) + f(t)$$
which I want to solve for $f(t)$ and $g(t)$. I also have initial conditions that $f(0)=g(0)=1$. How do I go about this in the best way?