InterviewSolution
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InterviewSolution
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If `y_(1)(x)` is a solution of the differential equation `(dy)/(dx)-f(x)y = 0`, then a solution of the differential equation `(dy)/(dx) + f(x) y = r(x)` isA. `y = (1)/(y_(1)(x))int r(x) y_(1)(x) dx +(c)/(y_(1)(x))`B. `y = y_(1)(x) int (r(x))/(y_(1)(x))dx + c`C. `y = int r(x) y_(1)(x) dx + c`D. None of these |
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Answer» Correct Answer - A `(dy)/(dx)-f(x)*y=0` `therefore" "(dy)/(y) = f(x) dx` `therefore" "In y = int f(x) dx` `therefore" "y_(1)(x) = e^(int f(x) dx)` Then for given equation, I.F `= e^(int f(x) dx)` Hence, solution is `y*y_(1)(x) = int r(x)*y_(1)(x) dx + c` `y = (1)/(y_(1)(x)) int r(x) * y_(1)(x)dx + (c)/(y_(1)(x))` |
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