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Maths-

General

Easy

Question

Equation of the curve passing through (3, 9) which satisfies the differential equation $fraction numerator d y over denominator d x end fraction equals x plus 1 over x squared$ is

$6 x y = 3 x^{2} - 6 x + 29$
$6 x y = 3 x^{2} - 29 x + 6$
$6 x y = 3 x^{2} - 29 x - 6$
None of these

hint Hint:

In this question, we have to find the equation of the curve passing through (3, 9) which satisfies the differential equation $fraction numerator d y over denominator d x end fraction equals x plus 1 over x squared$ . Firstly, we will integrate both side of the equation given and then substitute the value of point to find c. And later substitute the value of c in the differential equation to find the integrated equation.

The correct answer is: $6 x y equals 3 x squared minus 29 x minus 6$

$fraction numerator d y over denominator d x end fraction equals x plus 1 over x squared I n t e g r a t i n g space b o t h space s i d e s comma space w e space g e t colon rightwards double arrow integral d y equals integral open parentheses x plus 1 over x squared close parentheses d x rightwards double arrow y equals x squared over 2 minus 1 over x plus c space space _ _ _ _ _ _ _ _ _ _ _ _ e q u a t i o n space 1 A s space p o i n t space left parenthesis 3 comma 9 right parenthesis space s a t i s f i e s space t h i s comma space t h e n rightwards double arrow 9 equals 9 over 2 minus 1 third plus c rightwards double arrow c equals fraction numerator 54 minus 27 plus 2 over denominator 6 end fraction rightwards double arrow c equals 29 over 6 S u b s t i t u t i n g space v a l u e space i n space e q u a t i o n space 1 comma w e space g e t colon rightwards double arrow y equals x squared over 2 minus 1 over x plus 29 over 6 rightwards double arrow y equals fraction numerator 3 x squared minus 6 plus 29 x over denominator 6 x end fraction rightwards double arrow 6 x y equals 3 x squared plus 29 x minus 6$

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