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:
159
Step-by-step explanation:
10^2+(3+5)^2-5
-> 100 + (3+5)^2 -5
-> 100 + 8^2 - 5
-> 100 + 64 - 5
-> 159
(32•7a3b2)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "^-4" was replaced by "^(-4)".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
0-(((9•(a2))•(b6))•(0-7ab(-4)))
Step 2 :
Equation at the end of step 2 :
0 - ((32a2 • b6) • -7ab(-4))
Step 3 :
Final result :
(32•7a3b2)
I think its like this ,Tho hope it helped
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4:10 was when he started history
What are you supposed to solve
