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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It would be more than one because 3/5 + 3/4 equals 1 7/20
Answer:
Measure of side YX is 22 units.
Step-by-step explanation:
Since ΔVWZ ~ ΔXWY, their corresponding sides will be in the same ratio.
![\frac{VW}{XW}=\frac{VZ}{XY}=\frac{WZ}{WY}](https://tex.z-dn.net/?f=%5Cfrac%7BVW%7D%7BXW%7D%3D%5Cfrac%7BVZ%7D%7BXY%7D%3D%5Cfrac%7BWZ%7D%7BWY%7D)
By substituting the values given in the picture in the ratio,
![\frac{45}{30}=\frac{(3x-9)}{(x+8)}=\frac{36}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B45%7D%7B30%7D%3D%5Cfrac%7B%283x-9%29%7D%7B%28x%2B8%29%7D%3D%5Cfrac%7B36%7D%7B24%7D)
![\frac{(3x-9)}{(x+8)}=\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%283x-9%29%7D%7B%28x%2B8%29%7D%3D%5Cfrac%7B3%7D%7B2%7D)
By cross multiplication,
2(3x - 9) = 3(x + 8)
6x - 18 = 3x + 24
(6x -18) + 18 = 3x + 24 + 18
6x - 3x = (3x + 42) - 3x
6x - 3x = 42
3x = 42
x = ![\frac{42}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B42%7D%7B3%7D)
x = 14
m(YX) = x + 8
= 14 + 8
= 22
Therefore, measure of side YX is 22 units.
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