Question

the partial intregral of y"+y' +y =sin2x​

Answer 1

Answer:

y′′+y′+y=sin2x

I don't know what format the particular solution has. Once I know that, I can probably solve the problem with little difficulty. I haven't seen any examples in my textbook or else where with a exponential trig function on the right side. Using the format y=Asin(x)+Bsin(x) (and therefore y′=Acos(x)−Bsin(x), y′′=−Asin(x)−Bcos(x)) and substituting these values for y and its derivatives doesn't give me any value with a sin2x in it.

What format does the specific solution have? How is this sort of equation supposed to be solved?

The solution of the characteristic equation r2+r+1=0 is (r+0.5)2+0.75=0 is r=0.866i−0.5; then yc=e0.5x(Acos0.866x+Bsin0.866x) , but I don't know if this is is useful or at all how this is to be applied.

Step-by-step explanation:

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