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solve the following differential equation (1+y^2)(1+logx)dx+xdy=0

solve the following differential equation (1+y^2)(1+logx)dx+xdy=0

Grade:12

1 Answers

Nandana
110 Points
4 years ago
hi ,
 we can solve this problem by simple variable seperable method as follows –
      (1+y^2)(1+logx)dx = -x dy
        -(1+ log x) dx / x = dy / (1+y^2 )
               integrate on both sides w.r.t. corresponding variables
          – (∫1/x dx + ∫ logx /x dx) = ∫1/ (1+y^2 ) dy
             – (log x +1/2 (log x)^2 ) = tan ⁻¹ (t) + K
                       tan ⁻¹ (y) + log x +1/2 (log x)^2 +K =0 is the answer for this question .
                                                                            Thank you ...
 
 

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