The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
For more information about differential equation, visit
brainly.com/question/18760518
Answer:
Stop and save is the best
Step-by-step explanation:
I say this because your getting the same apples for cheap not only are they cheap but your also getting more.
First number = X
Second number = 8X
Third number = X - 3
The equation would be
X + (8X) + (X - 3) = 207
X + (8X) + (X - 3) = 207
X + 8X + X - 3 = 207
10X - 3 = 207
10X = 207 + 3
10X = 210
X = 21
First number = 21
Second number = 8 * 21 = 168
Third number = 21 - 3 = 18
Step-by-step explanation:
I think this might help
Answer:
(1/7, 1)
Step-by-step explanation:
By "answer," you probably meant "solution." What is the "solution of the system of linear equations
- 5y = - 5
+ 7x +6y=7
The first eqation can be solved for y: y = 1. Substitute 1 for y in the secon equation. Then 7x + 6(1) = 7, or 7x = 1, or x = 1/7.
The solution to this system is (1/7, 1)
