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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Slope is 2 because it goes up by two and over by one
Answer:
(10-8) + n
Step-by-step explanation:
Good luck with your work!
The answer is the second answer choice, an = -13 + 5(n - 1)
In this question, we would be multiplying.
In this case, you would multiply 20000 by 1.9, since 1.9 is the decimal form of 190%.
Solve:
20000 · 1.9 = 38,000
Answer:
38,000
