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.
Answer:
True
Step-by-step explanation:
Each x input has 1 y output
Answer:
The total price for ant farm is $12.84
Step-by-step explanation:
The price of ant farm = $ 12
The sales tax on the price = 7%
Noe, 7% of $12 = 
⇒The tax amount on the price = $0.84
So, the Taxed amount = The original price + Tax
$ 12 + $0.84 = $12.84
Hence the total price for ant farm is $12.84
Answer:
(8/5 , -2/5)
Step-by-step explanation:
x-y=2
2x+3y=14
-y=-x+2
y=x-2
2x+3(x-2)=14
2x+3x-6=14
5x-6=14
5x=8
x=8/5
y=(8/5)-2
y= -2/5
