We can reduce the order of the ODE by substituting , so that and . Then
has characteristic equation
with root , which has multiplicity 2, so that the characteristic solution is
Integrate both sides to solve for :
Integrate again to solve for :
And one last time to solve for :
Answer: six and three hundred twenty four thousandths
The formula to find the discriminant equals D = b^2-4ac.
(Quadratic equations have the formula ax^2+bx+c. A = -1, B = +4, C = -2.)
D = 4^2-4(-1)(-2). 8-8 = 0.
0 = 1 solution
-D = 0 solutions
+D = 2 solutions
The discriminant equals 0, also establishing that if you were asked to find the solutions, there would only be one.
Answer:
It would be negative
Explanation:
Y=5x
IS the equation that represents the cost for x movies, when each is $5