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:
10 minutes
Step-by-step explanation:
Since you can do 6 flyers each minute, the rate would go at 6x, with x being minutes. You initially did 80, so the equation for you would be y=6x+80.
Your friend's equation would be y=4x+100, because he initially had 100 done and is now getting 4 done per minute.
If you put the 2 equations in your calculator, the intersection will happen at x=10, showing that you and your friend will have an equal number of flyers at 10 minutes.
Answer:
62
Step-by-step explanation:
using the order of PEMDAS, you solve 8*9 and 2*5 first, then subtract them. so it will become 72 - 10, which is 62
hope this helps!
Answer:
28x=y
Step-by-step explanation:
28x=y because 14x-y=-14 plus y on both sides=
14x=-14y then add 14 to both sides=
28x=y
Answer:
-6
Explanation: use a calculator lol
