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
nami , 8 Years ago
Grade 12
Differential Calculus> solve the following differential equation...
1 Answers
Nandana
Last Activity: 8 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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