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2 years ago

Solve (D*D + 4)y = x + cos²x

Mathematics

1 answer:

Sedaia [141]2 years ago

7 0

Answer:

(D^2 + 9)y = cos 2x….(1). The corresponding homogeneous equation is (D^2 +9)y= 0,…(2), whose auxiliary equation is m^2 + 9 = 0, which has (+/-)3i as roots. The general solution of (2) is y = A.cos(3x) + B.sin(3x). Now to get a general solution of (1) we have just to add to the above, a particular solution of (1). One such solution is [cos(2x)]/[-2^2 +9] = (1/5).cos 2x. Hence a general solution of the given equation is given by y = A.cos(3x) + B.sin(3x) + (1/5)cos(2x), where A and B are arbitrary constants. The above solution incorporates all the solutions of the given equation.

Step-by-step explanation:

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Solve (D*D + 4)y = x + cos²x​

Solve (D*D + 4)y = x + cos²x