Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
Step-by-step explanation:
firstly you will add
the red cars and non red cars together and which is 65
probability of the red car = 25/65
to the lowest form is the 5/13(D)
3: multiply the change per minute by how many minutes: 3.1x15=46.5. 5: Is your opinion, I can't tell you how to feel. But a negative times a negative is a positive, so if there is an even number of negatives no matter how many positives there are it will be positive, if there is an odd number of negatives it will be negative. :) Hope this helps!
The radius r used in below equations would equal 2in because it is half the given diameter of 4in.The volume of the cone would be The volume of a cylinder with the same dimensions would be the cylinder is 24 - 8 = 16 cubic inches greater.
