Answer:
2 mph
Step-by-step explanation:
time = distance / speed
Let c represent the rate of the current. Then the upstream rate of the boat relative to the shore is (5c -c) = 4c, and the <em>upstream time</em> is ...
... 12/(4c) = 3/c.
Likewise, the downstream rate is (5c +c) = 6c, and the <em>downstream time</em> is ...
... 12/(6c) = 2/c.
The <em>total time</em> is the sum of upstream and downstream times:
... 3/c +2/c = 2.5
... 5/c = 2.5 . . . . . . combine terms
... 5/2.5 = c = 2 . . . multiply by c/2.5
Answer: Yes, they both equal -7/2
Step-by-step explanation:
Answer:
Step-by-step explanation:


case~2

Answer:
Verified


Step-by-step explanation:
Question:-
- We are given the following non-homogeneous ODE as follows:

- A general solution to the above ODE is also given as:

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.
Solution:-
- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.
- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

- Therefore, the complete solution to the given ODE can be expressed as:

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

- Therefore, the complete solution to the given ODE can be expressed as:
