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:
Total number of coins in the bag = 5 + 4 + 5 + 2 = 16 coins
Number of nickels in the bag = 4
We have to find the probability that Marissa draws a nickels from the bag.
Probability is defined as the ratio of Number of "Favorable Outcomes" to "Total number of possible outcomes"
In this case total number of possible outcomes is the total number of coins which is 16.
Favorable/Desires outcome is drawing a Nickle from the bag which are 4 in number. So, number of favorable outcomes is 4
Therefore, the probability that she will draw a nickel =
Answer:
(-9.5,1,7)
Step-by-step explanation:
Option 3 (1/4 x 60) since 59 is close to 60 and 25% can be rewritten as 1/4
Answer:
4,224
Step-by-step explanation:
You only multiply the numbers outside the shape
