Answer:
Step-by-step explanation:
and
Step-by-step explanation:
One approach to solve this problem is first to solve for x in terms of t and then substitute this answere in .
Starting with
, we can use the separation of variables method.
, integrating
For solving the integral we use partial fraction decomposition method:
this leads us to the equation:
, as it can be seen, we can use this to construc a system of equations
- and,
from 1. we get and, from 2. we get .
Now
so, we get:
Now we end up with some easily solving integrals
, m is the integration cosntant.
, taking in count only positive values for x and K
then after solving for x we end up with the answer:
.
Now for , we subtitute our last result and get
, by using the separation of variables method:
, integrating
,
using the substitution method and letting
, our integral takes the form
, using partial fraction decomposition method we end up with
, leading us to
From this: and, , thus
, integrating
, remembering
, we get
, for y positive the answer is: