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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Since there is no base down payment or anything the equation i think would just be 35m = c
If there was say a one time payment of $20 and then the monthly payments it would look like 20+35m=C
I hope this helps :)
Answer:
The graph not have x-intercepts
Step-by-step explanation:
we know that
The x-intercept is the value of x when the value of y is equal to zero
we have
This is the equation of an absolute value in vertex form open upward
The vertex is the point (2,12)
The y-coordinate of the vertex is above the x-axis and the graph open upward
That means ----> The graph do not intersect the x-axis
therefore
The graph not have x-intercepts
<u><em>Verify</em></u>
For y=0
substitute in the equation
----> is not true
The left side of the equation cannot be a negative number
so
The equation not have solution for y=0
therefore
The graph not have x-intercepts
see the attached figure to better understand the problem