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:
WE are given that 
. Then, to now the first for terms, we must replace n by 1,2,3,4 respectively. Then
Note that as n increase, 
gets closer to 0. So, the limit of this sequence is 0.
Answer:
y=5x
Step-by-step explanation:
yes your correct
A)
Answer:
x = 50°
Step-by-step explanation:
the sum of the exterior angles of any polygon is 360°
2x-12 + 32 + 2x + x + 90 = 360
5x + 110 = 360
5x = 250
x = 50
