Suppose Levi\'s Luxury Shop has cash of $8,745, inventory of $36,287, fixed assets of $14,204, accounts payable of $66,410, and accounts receivable of $20,033. What is the current ratio? Solution Current ratio = current assets / current liabilituies current assets = 8745+36287+20033=65065 current liabilities=66410 =65065 / 66410 =0.98.

1. Suppose Lu = 0 is an Nth order homogeneous linear differential equation; so L is an Nth order
linear differential operator. Suppose Lu = 0 has N homogeneous solutions: uj for j = 1,...,N.
Show that u = Nj = 1 cjuj = c1u1 + c2u2 + ....+ cNuN are arbitrary constants,
is also a solution. Is this the general solution? Explain
Solution
Suppose Lu = 0 is an Nth Homogeneous linear differential equation
. Suppose Lu = 0 has N homogeneous solutions: uj for j = 1,...,N.
means we ahve Lu1 = 0
Lu2 = 0 ....Lun = 0
now we will write above equations as :
Lc1u1 = Lu2c2 = Lcnun = 0
now adding above equations :
Lc1u1+Lc2u2+....Lcnun = 0
L { c1u1+c2u2....cnun)= 0
means c1u1+c2u2...cnun is also a solution and this is general solution
u = Nj = 1 cjuj = c1u1 + c2u2 + ....+ cNuN are arbitrary constants, is also a solution.