InterviewSolution
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InterviewSolution
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Find the general solution of the differential equation `(dy)/(dx) = log(x+1).` |
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Answer» We have , `(dy)/(dx)=log(x+1)` `rArr dy=log(x+1)dx` `rArr int dy = int log(x+1)dx` [integrating both sides] `rArr y=int {log(x+1)*1}dx + C, ` where C is an arbitrary constant `={log(x+1)*x}-int(1)/((x+1)) *x dx + C " " `[integrating by parts] `=x log (x+1) - int ((x+1)-1)/((x+1)) dx + C` `=x log (x+1) - int {1-(1)/((x+1)) } dx + C` ` = x log (x+1)-x + log(x+1) + C` `=(x+1)log(x+1)-x+C.` Hence, `y=(x+1)log(x+1)-x+C` is the required solution. |
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