-a) Will the sum of all solutions to a first order linear non-homogeneous ODE also be a solution to the ODE? EXPLAIN. -b) if the solution to a homogeneous version of the non-homogeneous ODE (I.e., the non-homogeneous ODE but with its right side being zero) is added to a solution to the non-homogeneous ODE, will the sum of the two solutions also be a solution to the non- homogeneous ODE? Solution a) Let us consider the ODE du?x.

1. -According to the quantity theory of money, which variable in the quantity equation is most
stable
over long periods of time?
a. money
b. velocity
c. price level
d. output
-Which of the following statements about financial institutions is correct?
I. Financial markets are institutions that indirectly connect savers to borrowers.
II. Corporations use equity financing to borrow directly from savers in the bond market.
III. Financial intermediaries indirectly connect savers to investors.
IV. A corporation facing financial difficulty pays bondholders their due before stockholders
receive anything at all.
A. I and II only
B. I, II, III, and IV
C. II and III only
D. III and IV only
Solution
Quantity theory of money: The following assumptions are required for describing the quantity
theory of money:--
1.The velocity of circulation of money is constant.
2. Full employment is there in the economy.
3. Money supply is not created but autonomous.
4. Money is a medium of exchange always.
Based on the above assumptions the quantity theory of money is as below:
In a particular period money paid by all buyers is equal to money received by all sellers.
Symbolically, PT = MV
P = Average price level
T = Total volume of transactions
M = Total quantity of money in an economy
V = Velocity or average number of times each unit of money is used for transactions during the
period.
Since the velocity is constant, it is most stable over long period of time.

2. Option ‘b’ is correct.