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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4p-13p-p=-150
-9p-p=-150
-10p=-150
<u>p=15
Order of operations. Doing so turns it into a simple division equation.</u>
Answer: 48,60
Step-by-step explanation:
4x+5x=108
9x=108
x=108/9=12
12•4=48
12•5=60
Answer:
21
Step-by-step explanation:
the sum of the express of the summation of the notation
