InterviewSolution
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InterviewSolution
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हल करें : `(1+2x^(x//y))dx + 2e^(x//y) (1-x//y)dy=0` |
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Answer» दिया गया अवकल समीकरण है: `(dy)/(dx) =-(1+2e^(x//y))/(2e^(x//y)(1-x/y))` या, `(dx)/(dy) = -(2e^(x//y)(1-x/y))/(1+2e^(x//y))` .............(1) `x=vy` रखें, तो `(dx)/(dy) = v+y (dv)/(dy)` (1) से, `v+y (dv)/(dy) = -(2e^(v)(1-v))/(1+2e^(v))` `rArr y(dv)/(dy) = -(2e^(v)+2ve^(v))/(1+2e^(v)) -v = (-2e^(v)-v)/(1+2e^(v)) rArr int (1+2e^(v))/(v+ 2e^(v)) dv = -(dy)/y` `rArr log|v+ 2e^(v)| = -log|y| + log c = log c|y|` `rArr |v+2e^(v)| =c/|y| rArr |x/y + 2e^(x//y)|=c/|y|` `rArr x/y + 2e^(x//y) = +- c/y = k/y`, जहाँ `k = +-c` `rArr x+2ye^(x//y) =k` यही दिए गए अवकल समीकरण का अभीष्ट हल है| |
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