The answer is 27.3375%.
To calculate this, a multiplication rule is used. The multiplication rule calculates the probability that both of two events will occur. In this method, the possibilities of each event are multiplied.
So, we have three events occurring simultaneously:
1. set contains female singer: 45% = 0.45
2. set contains female singer: 45% = 0.45
3. set contains female singer: 45% = 0.45
Also, it should be taken into consideration that there are three set combinations:
female-female-male,
female-male-female,
male-female-female
So, the probability for one set of the song is:
0.45 × 0.45 × 0.45 = 0.091125
Therefore, the probability is multiple ways to achieve this pattern of songs):
3 × 0.091125 = 0.273375 = <span>27.3375%.</span>
I'll assume the ODE is
Solve the homogeneous ODE,
The characteristic equation
has roots at 
and 
. Then the characteristic solution is
For nonhomogeneous ODE (1),
consider the ansatz particular solution
Substituting this into (1) gives
For the nonhomogeneous ODE (2),
take the ansatz
Substitute (2) into the ODE to get
Lastly, for the nonhomogeneous ODE (3)
take the ansatz
and solve for 
.
Then the general solution to the ODE is
