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y1 = 2 cos(x) − 1 is a particular solution for y'' + 4y = 6...

y1 = 2 cos(x) − 1 is a particular solution for y'' + 4y = 6 cos(x) − 4. y2 = sin(x) is a particular solution for y''+4y = 3 sin(x). Using the two particular solutions, find a particular solution for y''+4y = 2 cos(x)+sin(x)− 4/3 . Verify if the particular solution satisfies the given DE.

[Hint: Rewrite the right hand of this equation in terms of the given particular solutions to get the particular solution] Verify if the particular solution you found satisfies the equation y'' + 4y = 2 cos(x) + sin(x) − 4/3 . If it doesn’t verify, conclude that a particular solution does not exist.

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