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:

Answer:
If 1/2 gallon covers 540 square feet, then 1 gallon will cover 1080 square feet.
Step-by-step explanation:
Answer:
<h2>

</h2>
Step-by-step explanation:

Write -13x as a difference

Factor out x from the expression

Factor out -10 from the expression

Factor out x-3 from the expression

Hope I helped!
Best regards!!
Answer:
43,582,779
Step-by-step explanation:
129 x 337,851 = 43,582,779