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:
3.
Step-by-step explanation:
Let's break it down.
Sparkles used 12 balloons total to make 4 balloon animals. Divide 12 by 4, and you will get 3.
What I did for part 2 of the equation, is I multiplied 4 and 5 by 3 to ensure the variable matched my calculations. 4x3 is 12, and 5x3 is 15. add 12 and 15, and you will get 27 total balloons.
1:24 and 2:20 and 3:30 and 4:16 and 5:12
The correct answer is the second option: plus or minus square root of 20
Hope this helped :)
