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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12/x = 15/8
96 = 15x
x= 6.4 or 32/5
Answer:
57 square feet
Step-by-step explanation:
Split the boxes into two parts.
One box measuring 11.5 ft long and 3 ft wide. (Box A)
The second box measuring 7.5 ft long and 3 ft wide. (Box B)
Area (figure) = Area of box A + Area of box B
Area of box A
3 × 11.5 = 34.5 ft²
Area of box B
3 × 7.5 = 22.5 ft²
Area of figure = 34.5 + 22.5
Area of figure = 57 ft²
