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)
For more information about differential equation, visit
brainly.com/question/18760518
Answer:
1 1/4
Step-by-step explanation:
3 1/8 - 1 7/8
I like to line them up vertically
3 1/8
- 1 7/8
---------------
We need to borrow from the 3
Take 1 from the 3 and make it 8/8
2 (1/8+8/8)
- 1 (7/8)
---------------------
2 (9/8)
- 1 (7/8)
---------------------
1 2/8
Simplify the fraction by dividing by 2 on the top and bottom
1 1/4
This means you should do 240*3/8 which is 90. so 90 times 240=21600
the answer is 216000km^2
(5b)(-3a)
= (5*(-3))(b*a) (combine like terms)
= -15ab
The final answer is -15ab~
10!=3628800
10-3=7
7!=5040
3628800/5040=720
