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:

Step-by-step explanation:
Cross multiply, isolate the variable, and divide by the coefficient to solve.

Plug back in to check.

Answer:
4 1/3
Step-by-step explanation:
12/3=4
1/3+4=4 1/3
To multiply fractions, you just multiply across so you'd do:
3 × 2 = 6
4 × 3 = 12
The answer is 6/12, but it asks for the simplest form so you can simplify to 1/2. I hope this helps!
Answer: <u><em>The first number is 8</em></u>
Step-by-step explanation: Let the three No. s be x, y and z respectively
given = x+ y+ z= 72
y=7x
z=7x-18
∴As we know x+ y+ z=72
i.e. x+7x+7x-18=72
15x=72+18=90
15x=90
x=90/15
∴x=8
∴y=7x
7×8=56
∴z=7x-18
56-18=38
∴<u><em>The first no. is x=8</em></u>
<u><em>The second no. is y=7x = 56</em></u>
<u><em>The third no. is z=7x-18 = 38</em></u>