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Find the general solution of the differential equations `(e^x+e^(-x))dy-(e^x-e^(-x))dx=0`A. ` y = log |e^(x)=e^(-x)|+C`B. ` y = log. |(e^(x)-e^(-x))/(e^(x)+e^(-x))|+C`C. `y= log|e^(x)+e^(-x)|+C`D. None of these |
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Answer» Correct Answer - b Given ` (e^(x)+e^(-x))dy - (e^(x)-e^(-x))dx = 0 ` ` rArr (e^(x) +e^(-x))dy = (e^(x)-e^(-x))dx` On seperating the variables , we get ` dy = ((e^(x)-e^(-x))/(e^(x)+e^(-x)))dx` On integrating , we get ` int dy = int ((e^(x)-e^(-x))/(e^(x)+e^(-x)))dx` Let `e^(x) +e^(-x) = t rArr (e^(x) -e^(-x)) dx =dt` ` :. int dy = int (e^(x) - e^(-x))/t (dt)/(e^(x)-e^(-x))=int 1/t dt` ` rArr y = log |t| +C` ` rArr y = |log| |e^(x) +e^(-x) | +C` |
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