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:

This is equivalent to:
(2.2533/2.59)(10^8/10^4)
(0.87)(10^4) which is:
0.87X10^4 which is equal to:
0.87X10000 which is equal to:
8.7X1000 and since 1000=10^3 we can say:
8.7X10^3
3/2 and 9/10. Look at the denominators. 2 times what number equals 10. That number would be 5. So if you multiply the first fractions denominator by 5 you get 10. Do the same to the top. you get a new fracrion which is 15/10. Add normally. 15/10 + 9/10 = 24/10. In lowest terms it is 2 2/5 (2 wholes and 2 out of 5)
The answer is 62/25.
Hope this helps.
2876 Rounds To 3000
513 Rounds To 500
18 Rounds To 20
Then multiply:
3000x500x20= 30,000,000
Hope i helped :)