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:
0.25 Hope this helps :)
Step-by-step explanation:
You add the 5 red and 3 green
8 Mables besides blue
so that's 2/8
simplified 1/4
1/4=0.25
3(x-1) = 2x - y
3x-3 = 2x-y
3x-2x+y = 3
x + y = 3 ----> (1)
2(x+y) = 3+3y
2x + 2y = 3 + 3y
2x + 2y - 3y = 3
2x - y = 3 -----> (2)
make equation (1) and (2) together
x + y + 2x - y = 3+3
3x = 6
x = 2
now make x = 2 in equation (1)
x + y = 3
2 + y = 3
y = 3-2
y = 1
(x,y) = (2,1)
