InterviewSolution
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InterviewSolution
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Solve `(x^(3)+x^(2)+x+1)(dy)/(dx) =2x^(2)+x, " given that " y=1 " when " x =0.` |
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Answer» Correct Answer - `y=(1)/(2){log|x+1|+(3)/(2)log (x^(2)+1)-tan^(-1)x}+1` `dy=(1)/(2){(1)/((x+1))+(3x-1)/((x^(2)+1))}dx " " `[by partial fractions] `rArr int dy=(1)/(2) int {(1)/((x+1))+(3)/(2)*(2x)/((x^(2)+1))-(1)/((x^(2)+1))}dx +C` `rArr y =(1)/(2) {log |x+1|+(3)/(2)log |x^(2)+1|-tan^(-1)x}+C.` When x = 0 and y = 1, then C = 1. |
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