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:
8-6i
Step-by-step explanation:
complex number in standard form will be in the form of a+bi
(-2 − 2i) + (10 − 4i) , open parenthesis
-2- 2i +10 -4i, group like terms
-2+10 -2i -4i, combine like terms
8 - 6i
Answer:
294
Step-by-step explanation:
Difference means subtraction, so you just subtract 533 from 827.
827-533=294
hope this helps! : )
Answer:
slope:3
y intercept:1
equation:y=3x+1
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
