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Q. The particular Integral of D.E. \( (D-1) y=x^{2}+5 x+7 \) is

Answer»

P.I. = \(\frac{1}{D-1}(x^2+5x+7)\) 

\(-\frac{1}{D-1}(x^2+5x+7)\)

= - (1+D+D2+D3+...) (x2+5x+7) 

(∵\(\frac{1}{1-D}\) = 1+D+D2+...)

= - ((1+D+D2)x2 + (1+D) 5x+7)

= - (x2+2x+2+5x+5+7)

= - (x2+7x+14).



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