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)
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Answer:
Step-by-step explanation:
TU , UV , VW, TW are the sides
As points T and U have same x-coordinate, length of TU will be given by the difference of y-coordinate
TU = 9 - 7 = 2 units
As points U and V have same y-coordinate, length of UV will be given by the difference of x-coordinate
UV = 5 - 2 = 3 units
As points V and W have same x-coordinate, length of VW will be given by the difference of y-coordinate
VW = 9 -7 = 2 units
As points W and T have same y-coordinate, length of WT will be given by the difference of x-coordinate
WT = 5 - 2 = 3 units
TU = VW = 2 units
UV = WT = 3 units
So, TUVW is a rectangle
Area = length *width = 3* 2 = 6 square units
Perimeter = 3 + 2 + 3 + 2 = 10 units
Substitute the 0 in for y:
-3x - 3(0) = -12
-3x - 0 = -12
-3x = -12
Divide by -3:
-12/-3= 4
Answer:
x = 4
