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
Answer:
This might be permutation promblem srry if im wrong.
P(6,3)=6x5x4=120
P(4,2)=4x3=12
Answer:
1,2,4
Step-by-step explanation:
Factors for 16: 1, 2, 4, 8, and 16.
Factors for 44: 1, 2, 4, 11, 22, and 44.
Answer:
x=56 and the exterior angle is 116
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.
y + 2x+4 =180
Solve for y by subtracting 2x+4 from each side.
y + 2x+4 - (2x+4) =180 - (2x+4)
y = 180-2x-4
y = 176-2x
The three angles of a triangle add to 180 degrees
x+ y+ 60 = 180
x+ (176-2x)+60 = 180
Combine like terms
-x +236=180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply each side by -1
-1*-x = -56*-1
x=56
The exterior angle is 2x+4. Substitute x=56 into the equation.
2(56)+4
112+4
116
Let
P1 = (x1, y1) = (4, 7)
P2 = (x2, y2) = (2, 3)
The first thing to do in this case is to find the distance between two points by the following equation:
d (P1, P2) = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
d (P1, P2) = root ((2-4) ^ 2 + (3-7) ^ 2) = 4.47
answer
The houses are separated 4.47 units.
