I have the following differential equation: $$ y'(t) = \frac{y(t)-7t}{y(t)+t}. $$
I would like to determine the second order Taylor polynomial that satisfies $y(-1)=3$.
I have defined the differential equation in maple as follows: $$ L := y'(t) = \frac{y(t)-7t}{y(t)+t} $$
I have used the following command to find the series solution:
dsolve({L, y(-1) = 3}, y(t), series, order = 2)
I do get the correct solution. However as I am also calculating by hand I would like to check my results so I would like to compute $y'(-1)$ and $y''(-1)$ directly in maple. How do I do that? I have tried but it simply is not working!
Thanks.