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Question Number 91384 by jagoll last updated on 30/Apr/20

$$particularintegral$$$$y^{″}+3y^{\prime }+2y=4\cos {}^{2}x$$

Commented by jagoll last updated on 30/Apr/20

$$PI\Rightarrow y_p=\frac{4\cos {}^{2}x}{D^2+3D+2}$$$$=\frac{4\cos {}^{2}x}{2D+3}=\frac{(2D-3)\left(4\cos {}^{2}x\right)}{-9}$$$$=-\frac{1}{9}[8(-\sin 2x)-12\cos {}^{2}x]$$$$=-\frac{1}{9}(-8\sin 2x-6-6\cos 2x)$$$$=\frac{8\sin 2x}{9}+\frac{6\cos 2x}{9}+\frac{6}{9}$$

Commented by jagoll last updated on 30/Apr/20

$$itcorrect?$$

Commented by 675480065 last updated on 30/Apr/20

$$\mathrm{ok}\mathrm{sir}$$

Commented by jagoll last updated on 30/Apr/20

$$aresure?$$$$$$

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