InterviewSolution
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InterviewSolution
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`(1 - x ^(2)) (dy)/(dx) + xy = x sqrt(1-x^(2))` |
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Answer» Correct Answer - `y = (-1)/(2) sqrt (1 - x ^(2)) log ( 1- x ^(2)) + C sqrt ( 1- x ^(2))` ` (dy)/(dx) + (x)/( (1- x ^(2))) * y = (x)/(sqrt (1 - x ^(2)))` ` IF = e ^(-(1)/(2)int (-2x)/((1- x ^(2))) dx) = e^(- (1)/(2) log ( 1- x ^(2)) = e ^(log"" (1)/(sqrt (1- x ^(2)))) = (1)/(sqrt (1- x ^(2))` `therefore ` its solution is `y xx (1)/(sqrt (1- x ^(2))) = int (x)/(sqrt (1 - x ^(2))) * (1)/(sqrt (1- x ^(2))) dx = (-1)/(2) int (-2x )/(( 1 - x ^(2))) dx + C ` `" " = - (1)/(2) log (1 - x ^(2)) + C`. |
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