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Question Number 136734 by mohammad17 last updated on 25/Mar/21

Answered by Ñï= last updated on 25/Mar/21

$$Q5:::$$$$y_p=\frac{1}{D^2+3D+12}(e^x\cos x-\cos x)$$$$=e^x\frac{1}{D^2+5D+13}\cos x-\frac{1}{D^2+3D+12}\cos x$$$$=e^x\frac{1}{5D+12}\cos x-\frac{1}{3D+11}\cos x$$$$=e^x\frac{5D-12}{25D^2-144}\cos x-\frac{3D-11}{9D^2-121}\cos x$$$$=\frac{e^x}{169}(12\cos x+5\sin x)-\frac{1}{130}(3\sin x+11\cos x)$$$$y=e^{-\frac{3}{2}x}(C_1\sin \frac{\sqrt{39}}{2}x+C_2\cos \frac{\sqrt{39}}{2}x)+\frac{e^x}{169}(12\cos x+5\sin x)-\frac{1}{130}(3\sin x+11\cos x)$$$$-------------------$$$$Q6:::$$$$y_p=\frac{1}{D^4+2D^2-228D}(2\sin x-x^2-2)$$$$=\frac{2}{51985}(228\cos x-\sin x)+\frac{1}{3}\cdot (\frac{x^3}{228}+\frac{6+6x^2}{{228}^2}+\frac{24x}{{228}^3}+\frac{48}{{228}^4})-\frac{1}{342}$$$$y=C_1+C_2{e}^{-6x}+(C_3+C_{4}x)e^{6x}+\frac{2}{51985}(228\cos x-\sin x)+\frac{x^3}{684}+\frac{x^2}{25992}+\frac{x}{1481544}$$$$$$$$???$$

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