To find the particular integral

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Hi

here is question with answer

please can help me from where we got

1 + 9

and

-2+9

help me please

Handwritten solution of the differential equation (D^2 + 9)y = e^x - cos 2x: auxiliary equation m^2 + 9 = 0 giving m = ±3i, then particular integrals e^x/(1^2+9) = e^x/10 and -cos 2x/(-2^2+9) = -cos 2x/5, and the general solution.
 
manal950 said:
Hi

here is question with answer

please can help me from where we got

1 + 9

and

-2+9

help me please

Handwritten solution of (D^2 + 9)y = e^x - cos 2x: auxiliary equation m^2 + 9 = 0 giving m = ±3i, then particular integrals e^x/10 and -cos 2x/5, with general solution y = C1 cos 3x + C2 sin 3x + e^x/10 - cos 2x/5.
What is [itex]\displaystyle \ \ \left(\text{D}^2+9\right)\left(Ae^x\right)\ ?[/itex]

What is [itex]\displaystyle \ \ \left(\text{D}^2+9\right)\left(B\cos(2x)\right)\ ?[/itex]